6 Ideation
Michelle Ferrier
“Creativity, as has been said, consists largely of rearranging what we know in order to find out what we do not know. Hence, to think creatively, we must be able to look afresh at what we normally take for granted.”
— George Kneller, author of The Art and Science of Creativity
How do you know if your good idea is the next big thing? Whether you are an intrapreneur, working within an existing business, or an entrepreneur looking to create a business startup, or a student creating an idea for a class project, this question is the one that should drive you to find answers. Unfortunately, it is not a question that can be answered on its own. It takes answering a bunch of other questions of your potential customers, of your own motivations, and of your idea as well. Two key qualities required to begin this journey include curiosity and creativity. As a communicator or a student at a mass communication program, you should already possess an innate curiosity about people, storytelling, and problem solving. Creativity is a skill that can be cultivated as an individual or as part of group or team exercises, to develop unusual connections, breakthroughs in processes, or insights that lead to product development. Often, the journey to a good idea begins with asking “What if?”
Ideation is the process of coming up with an idea. It is using creativity and questions like “What if?” to imagine ways something can be done differently. The ideation stage is critical to ensure that you are generating good ideas from the start. It involves seeing problems and opportunities, brainstorming around the problems you identify, and doing research to test your assumptions about the market, your customers, and your idea. Refining that initial idea involves assessing the market, looking at trends, and asking questions (and more questions)—and learning from potential customers, investors, and research whether your idea is a good one. The design process consists of a series of steps to test assumptions and ideas. Ideation falls within a larger design process that begins with understanding who you are serving; empathizing, understanding, and defining the needs of that target audience; then ideating around what is needed (Figure 1):
In the Stanford School Design Thinking Process, there six stages to design[1]:
- Empathizing
- Defining
- Ideating
- Prototyping
- Testing
- Sharing
According to 2012 research by Harvard Business School instructor Shikhar Ghosh, 75% of venture-backed startups fail.[2] Ideas are like opinions—everyone has one. If the founders of those failed companies could have answered that question as to whether their idea was the next big thing…well everyone wants that guarantee. But entrepreneurship is risky. Startups are risky. You and your team are using your time and your intellectual property (ideas) to create something new. Generating a great idea from the start is part of a larger set of success factors such as the expertise of the founders, the competitive landscape, speed to market, and other factors.
These other success factors include:
- The composition of the team itself;
- The execution of the concept. Is the team adaptable, effective and efficient?
- The structure or business model shows a clear revenue path and immediate revenue stream;
- The structure of funding; and
- The timing of the idea and its entry into the marketplace.
What ultimately matters most is not the idea, but the ability of the team to work together, execute and test an idea, and get their idea out into the marketplace. So the ideation stage is about minimizing the risk of failure by coming up with ideas that the world needs or wants. Successful startups begin with a quality idea, one that is novel, encapsulates a “truth,” and will have good barriers to competitors.
Students will often come to me and say, “I’ve got this great idea, but I’m afraid to share it because someone might steal it.” I often coach students that their fear is preventing them from finding other teammates, coaches, potential investors, and mentors. Timing and execution are king; ideas, well, everyone has one. So if you’re hoarding your ideas, you are limiting one of your key assets, which is timing.
Is an idea something that can be protected? Ideas themselves cannot be copyrighted, but original expressions of ideas in a tangible medium can earn legal protection. Review the following resources to understand what can and can’t be protected under U.S. copyright, patent or trademark law.
- FAQs About Copyright, United States Copyright Office, https://www.copyright.gov/help/faq/index.html[3]
- Patent FAQs, United States Patent and Trademark Office, https://www.uspto.gov/help/patent-help[4]
- Trademark FAQs, United States Patent and Trademark Office, https://www.uspto.gov/learning-and-resources/trademark-faqs[5]
But what if you don’t have a great idea? How do you practice stretching your imagination to be more creative? And what is creativity anyway? A recent article in the alumni magazine for the University of Central Florida[6] spoke to the entrepreneurial culture that has been a part of the DNA of the institution since its founding as a technical school in 1963. Administrators and faculty from all types of disciplines were asked to weigh in. Michael Pape, Dr. Phillips Entrepreneur in Residence, says creativity is the hunt for an answer to a secret:
“Creativity is a process of bringing something new into existence that challenges prevailing assumptions. It’s fundamental to human existence. To challenge prevailing assumptions, you need to discover secrets.” Pape says “to observe, embrace chaos, and try to frame it into form, you might uncover those secrets in the process.”
Rick Hall, production director for the Florida Interactive Entertainment Academy, says that creativity is a teachable skill.
“Creativity is really just your ability to associate two disparate ideas in a way that others haven’t thought of before. You’ve got to proceduralize creativity. And never let a good mistake go to waste.”
I once interviewed a student at the University of Pittsburgh who got involved in entrepreneurship because he thought himself to be someone who was creative.
“I always wanted to pursue new ideas,” he said. “It just seemed like the current system is kind of rigid in the sense that the older you get, the more you have to start pruning away some of your ideas and get a more precise focus. And for me, I kind of like things open-ended, and I like to really explore all these ideas that I feel is like part of one big puzzle. And when you put that together, that’s how you get the best products because it draws from a number of inspirations.”
Scanning the Environment
Pape says the creative process begins with observation. As a curious journalist, I am always on the lookout for problems, opportunities and new ideas, observing what is happening around me, listening to what my neighbors are talking about, and what people are struggling with in their everyday lives. And as Hall suggests, we can “proceduralize creativity” by increasing the juxtapositions, the opportunities for the collisions of disparate ideas that might spark the next idea.
As an avid reader and a bit of a science geek, I am always scanning publications inside and outside my field that feature innovations in science, medicine, technology, and journalism such as Wired, FastCompany, and Scientific American. First, I’m learning about innovations and how others leveraged their ideas into businesses. Second, I’m learning how founders adapt their ideas as they learn. Third, I begin to see the world through others stories, experiences, and disciplines that help me to “look afresh” at the world as George Knelle suggests.
Scanning the environment like this is what led me to create Troll-Busters.com in 2015 as I observed what was occurring in social media spaces online and the challenges of women journalists and journalists of color in maintaining a voice online in the midst of targeted online harassment. While the idea began because of my own personal experience and the current news of Gamergate attacks,[7] I quickly validated that this was a common experience among journalists and media organizations. The idea for TrollBusters was validated initially by the response from female journalists themselves at a hackathon. However, we quickly began diving into global scholarly research that further pointed to the scope and scale of the problem we were addressing.
Through deep interviews with women journalists, we discovered a reluctance to report abuses and a lack of knowledge about what to do next after an attack. The interviewees also talked about the lack of support from peers and management. We started by developing awareness campaigns and online courses that made visible what was happening all over the world and helped women journalists take control of their own protection and speak up about the online harassment they are experiencing.
Look to the work of futurists and others who attempt to predict the future of technology, education, manufacturing, and other fields. Amy Webb,[8] founder of the Future Today Institute, examines trends in technology, media, and communications. In her new book, The Signals are Talking,[9] she says there are “signals” that everyone can watch for, beyond what is covered in the technology press. She says “It’s not like there’s a singular source where you would go to find the unusual suspects at the fringe. Instead, it’s a series of guiding questions she uses in her explorations:
- Who do I know of that’s been working directly and indirectly in this space?
- Who’s funding this work?
- Who’s encouraging experimentation?
- Who might be directly impacted if this technology succeeds one way or the other?
- Who could be incentivized to work against any change?
- Who might see this technology as just the starting-off point for something else?”
Then the curious, like Amy, get going. They start asking questions. And reading. And listening.
The New Media Consortium started asking these questions of its employees, who were trying to keep up with the changing technology landscape. They realized that many policy makers, industry leaders, innovators, educators, and others struggled to keep up with technology trends. They started the NMC Horizon Project[10] to chart emerging technologies and their implications for teaching, learning, and creative inquiry. (Note: They have ceased operation, but the reports[11] are still available. Accenture, a strategy and consulting company, creates a technology trends report. Its 2017 Technology Vision[12] report details disruptive technology trends and deep industry knowledge. CBInsights tracks trends across multiple industry sectors including automotive, financial tech, the Internet of Things, artificial intelligence, AR/VR, and other technology areas.
In the media field, I’ve mentioned publications like Wired and FastCompany that provide a deep dive into media and technology innovations. The Pew Research Center[13] offers deep research into social, religious, technology, and media trends and usage. Other media-focused publications include MediaShift, TechCrunch, Mediagazer, and VentureBeat.
CrunchBase is a database of startups, product development timelines, funding rounds, and other information. Add in subscriptions to online newsletters for the startup and entrepreneurship world like Entrepreneur and Fast Company, Inc. and others to keep an eye out on emerging, competing ideas in the market. Find these types of sources and scour them to cultivate new ways of seeing the world, the first step to creating innovative ideas.
Thinking Creatively With Human-Centered Design
LUMA Institute defines human-centered design: “Human-Centered Design (HCD) is the discipline of developing solutions in the service of people.”[14] Human-centered design (HCD) is being adopted now by more organizations, strategists, and development practitioners and has been taught in places like Stanford’s D-School (Design School). HCD views people as the core focus of design and development. According to LUMA Institute,[15] which works with organizations seeking to innovate:
“Every story of a good innovation — whether it’s a new product, a new service, a new business model or a new form of governance — begins and ends with people. It starts with careful observation of human needs, and concludes with solutions that meet or exceed expectations.”
When I teach innovation, I separate the Human-Centered Design process into three phases:
- Inspiration Phase: Learn directly from the people you’re designing for as you immerse yourself in their lives and come to deeply understand their needs.
- Ideation Phase: Make sense of what you learned, identify opportunities for design, and prototype possible solutions.
- Implementation Phase: Bring your solution to life and eventually to market. And you’ll know that your solution will be a success because you’ve kept the very people you’re looking to serve at the heart of the process.
Individuals, teams, and other groups use brainstorming and ideation to come up with better ideas — ideas that speed processes, ideas that create new products, ideas that create innovations, and ideas that solve problems. But usually that activity happens in a vacuum —a team sits around a whiteboard coming up with ideas. With human-centered design, inspiration comes through exploration of actual people, their problems, and their needs. So ideation is like an incubator for experimentation. The better you become at asking questions of potential customers and getting them answered quickly, the better you can be at shaping your idea into something that meets a need.
Ideation also involves knowing your outcome/deliverable. If you are creating ideas for a student competition, you’ll want to know the rules and what the judges will be evaluating. Some competitions give you the problem you are attempting to solve. Your measure of success will be in how closely your idea aligns with the competition goals. I’ve often judged student competitions where there are different rubrics. The simplest I’ve used asks founders to ask themselves three questions:
- Feasibility: Can we do this?
- Viability: Should we do this?
- Desirability: Do they want this?
The most valuable design sits at the intersection of these three questions and will help guide you in positioning your ideas to meet market needs.
The rubric I developed for an international innovators cup competition provides a good template to use to determine if your idea is innovative:
- Presentation was compelling, easy to understand, and described the problem and a “fresh” solution.
- Meets the threshold for innovation. Judges should be guided by the reality that truly transformational innovation is rare. Incremental innovation is more the norm but is equally valuable in our competition so long as it provides an inspired solution to the challenge that has been posed.
- Takes full advantage of new media tools, platforms, technologies, and applications in use today. These might include things like interactive design, gaming, geolocation-based tools, informational graphics, and all aspects of social media, etc.
- Addresses the problem within its context. It should demonstrate that it is offering an idea or approach that is supported by facts and/or research and demonstrates an understanding of today’s media and communication landscape, including familiarity with any similar products, apps, or services.
- Understands possible roadblocks, competition, and need for a sustainable advantage. The solution shows an understanding of the roadblocks that need to be overcome, the competition, and how the solution can be sustainable.
- Provides a solution that clearly describes its main features and benefits and presents a valid value proposition with the key activities clearly outlined.
I also added this “diversity enhancement” component to the competition questions to ensure student teams thought about and integrated the needs of underserved and underrepresented users/customers/audiences in their solutions.
- Solution embraces diverse viewpoints, populations, or audiences. The solution realistically includes the potential to expand media diversity, including serving underserved populations:
Later in the chapter, we’ll look at specific team exercises to get your group thinking expansively, increasing the juxtaposition of disparate ideas, and generating ideas that we can test. But first let’s examine the media landscape and see if we can find interesting juxtapositions and questions that can help us find novel ideas.
The Media Innovation Landscape
Media innovation and entrepreneurship brings together journalism, technology, and business to create new projects inside and outside of traditional media organizations. For the media industry, there are significant opportunities in the disruption to business models and technological changes. This seismic shift in the monolithic news and information business has created a landscape that has allowed new forms of journalism and technology to emerge, driven by innovation, creativity, and entrepreneurship. The report “The Big Thaw: Charting a New Future for Journalism” by Tony Deifell of Q Media Labs[16] details the new competitive landscape for today’s media enterprises (Figure 3).
As Deifell’s report describes, this disruption can be seen as opportunity. Each of the four areas: new competitive landscape, new sources of value, new distinctive competencies, and new business models presents challenges, questions, and spaces providing fertile ground for new ideas. His four questions challenge us to continue to look to the media industry and communication professions for opportunities by asking ourselves:
- How are media organizations structured to capture value?
- What needs can be met, problems solved, or desires fulfilled?
- How is the landscape changing?
- What new capabilities are needed to succeed?
For example, look under “New Competitive Landscape.” The media industry has had to respond to new devices and convergences. Existing companies have had to innovate and design products to maximize the mobile experience for users of their content and products. Think about news apps such as BBCNews[17] for traditional news entities that expanded their existing brand into a new device. We can also point to startups like FlipBoard,[18] a tool designed solely to solve the problem of making reading content easier on a mobile device. Mike McCue, the founder of FlipBoard, says he never intended to start another company after he sold his prior company TellMe to Microsoft. His new company started by asking the question “What if?” that started him thinking about redesigning the web interface from scratch.
The mashup of disciplines and technology yields new forms of media entrepreneurship. The chart from The Big Thaw: Report on New Competitive Landscape, p.11 (Figure 4) shows the new media paradigm that is driving these changes.
It was at the intersection of three disciplines — business, nutrition, and journalism — that I developed the idea for LocallyGrownNews.com, which won a News Media Women’s Entrepreneur grant of $20,000 from the McCormick Foundation in 2009. The idea — Women’s Community News Franchise — provided the infrastructure—technical, education, writing, publishing, software, and advertising support — to develop online community news and information franchises. Citizen journalists and community members can focus on what they are most passionate about — building their community conversation through good local information and networking.
The business structure for LocallyGrownNews.com came from the franchise business model of providing services and growing a prototype model. The content topic came from the local food movement that was gaining favor nationwide. Geography and journalism became my way to solve the problem of access to fresh, local food. How could I help people live a local food lifestyle through LocallyGrownNews.com? By providing a website with information about local producers, farmers markets, and timely alerts of seasonal goods, I was able to solve the problem of getting good information about the local produce market to my audiences. I’d found a niche at the intersection of the growing local food movement, distributed networks of content creators, services, and a need for good information.[19]
Defining the Problem Space
Before you design a solution, you need to know what problem you are trying to solve. I often have students who want to create startup ideas that solve a personal problem. One of my students wanted a better way to share music. Another wanted to create a way to earn Boy Scout merit badges online. However, each of these students needs to define the problem space to determine whether their solutions—online education and peer-to-peer recommendations—were really a problem for other people. In other words, is this problem a pain point for just you or are there others? Is there a real problem with a large enough market that needs a solution? To define the problem space, we need to start with a more expansive view of what we are dealing with to determine what might be the best solution.
Remember the three questions we asked earlier in the chapter?
- Feasibility: Can we do this?
- Viability: Should we do this?
- Desirability: Do they want this?
At this point in the process, we are trying to answer the desirability question…Do they want this? So we have to define who is the “they” in this question, and then brainstorm to discover the “this” or solution in the question we want to test. We can use human-centered design to experiment and match our solutions to customer needs at the sweet spot in the center of feasibility, viability, and desirability.[20]
Working the Problem Space
So let’s say you are trying to develop concierge college admissions services. That’s the business you want to create. But what is the problem you are trying to solve? Often, students jump to a solution before diving deeply into understanding the problem space. Who is experiencing pain? Is it painful enough that people are seeking solutions and willing to shell out money?
Stanford University’s D-School has developed exercises for brainstorming and developing ideas. LUMA Institute and IDEO.org are two additional companies that help organizations think more expansively and deliver ideas that meet human needs.
Stakeholder Mapping
To visualize who is impacted by the problem you are trying to solve, you can use a stakeholder map to get a sense of the problem space, the actors in it, and who your solutions might address.
For example, students in a social media class were attempting to create tools and strategies to reach out to potential undergraduate students for college admissions. Of course, they started with the pain points and perspective of high school students having recently been in the search for colleges themselves. However, by identifying other stakeholders that play a role in the admissions process, the students were able to identify other pain points and possible solutions that addressed parents, admission counselors, and other stakeholders in the map (Figure 6).
To begin, you need stickies and limited drawing ability. Also a large blank canvas of paper.
- Create small teams of two to six people. Each person in the team gets sticky notes and a marker.
- Independently, team members are invited to brainstorm potential stakeholders in the problem space. In our example above, we went beyond the college organization to look at the role of parents, high school counselors, government agencies, and others play in the college decision process. Individual work should be given about one minute.
- Collectively, the team goes through its stakeholders, identifying commonalities and defining the roles more clearly by adding a visual element or a speech bubble to suggest what the person may be saying or thinking. These stakeholder stickies are put up on the blank canvas by consensus of the group.
- Organize the stakeholders by grouping entities that are linked by geography or processes. Use lines to draw relationships between stakeholders. For example, a line between parents and the financial aid office of a college might be drawn with dollar signs on it.
- Discuss in the group where there are breakdowns, pain points, and other places where innovation might help to solve the problem. These discussions can then be used to refine who the customer might be for your efforts — students, parents, college administrators, etc. — and who will pay for your solution.
- Select the stakeholders that you will continue to ideate around as potential customers.
Statement Starters
One exercise, found at LUMA Institute,[21] is designed to ask “What if?” types of questions: open-ended questions that become the jumping point for brainstorming. Sample statement starters include: What if_____? or How might we_____? These statement starters are then attached to the problems you’ve identified in your stakeholder mapping exercise. Brainstorming then happens around the problem you’ve identified.
IDEO has a design kit[22] with many examples.
Other Tools You Can Use
- IDEO’s Design Kit resource[23] will help you work with students in brainstorming exercises like the Mash Up which encourages students to think outside of the box to create brilliant proposals and solutions.
- Check out this collection of Human-Centered Design methods[24] you can use to guide students in the ideation phase.
- LUMA offers an online platform[25] to help people implement Human-Centered Design using LUMA’s “flexible, repeatable and easy-to-learn” system of Human-Centered Design.
- Exploring your hunch[26] is a huge part of Human-Centered Design. Here is a useful tool to get those ideas and creative juices flowing by exploring and testing your hunch.
- The card game Aha![27] created by the City University of New York allows students to juxtapose an emerging technology with an audience or need.
- Help students to prioritize, communicate, and strategize using this synthesis tool and team activity.[28]
- Try these pointers to structure and organize brainstorming sessions[29] to ensure they are truly engaging, meaningful, and successful.
Validated Learning
Eric Ries of The Lean Startup advocates “failing fast.” What he’s suggesting is that teams quickly move through the ideation stage to customer discovery and testing phases, tossing out assumptions and ideas that fail to meet customer needs.
IDEAS → BUILD (CODE) → MEASURE (DATA) →LEARN
You and your team will engage in a process of validated learning…confirming your assumptions through user testing, research, interviews, or ethnography. You may also build test sites or “smoke tests”—fake websites that walk users through the solution to see if they will pull out their wallet and buy (but don’t use your real domain name for these tests). You may pivot or change ideas after getting feedback or may find yourself back at the empathy stage, gathering more information about the problem space before creating new solutions. The idea is to stay lean and iterate quickly through ideas: build, measure, and learn.
With validated learning, you can test your value hypothesis — the value proposition that you are offering to your customers — or your growth hypothesis, how you intend to scale your company by testing new markets, or types of users. A hypothesis template looks like this:
We believe that ______ will cause [the users] to [do this action/behavior] because of [value proposition].
An example might be:
We believe that an augmented reality shopping app will cause brick-and-mortar shoppers to walk into stores more frequently because of the urgency and proximity of the deals and discounted offers.
Hypotheses are tested using the traditional research methodologies and a prototype or minimum viable product (MVP) of your idea. A prototype is a reduced version of your actual product or service, featuring just key features or functions. Version One of your product has every feature and function that users might need. A prototype can be developed in a few hours or days, while your first full version may take months.
Your team will define the hypothesis, determine how you will test the hypothesis, and assess what you learned from the results. Developers use A/B testing to try two different solutions and see which one gets the best response. This testing might be two different designs of a home page, testing color schemes or even two different solutions.
Before you spend valuable time and money rolling out a product that no one needs, a prototype and idea testing can help refine your ideas and discard or enhance your product or service features.
SWOT Analysis
Once you have identified the problem your group intends to solve, you must ask if another product already addresses it. If so, how? Conduct a SWOT (Strengths, Weaknesses, Opportunities, and Threats) analysis from the point of view of the competition. (Download a free worksheet.[30]) Do this for each close competitor, large or small, until you clearly identify your niche and are able to refine your target market.
Resources for Students and Faculty
READINGS
Links to articles that describe brainstorming, ideation, and design thinking.
- The Creativity Imperative in the Innovation and Entrepreneurship Curriculum: A Dilemma in the Scholarship of Teaching[31]
- Fostering Creativity – a Holistic Framework for Teaching Creativity[32]
- A Taxonomy of Innovation[33]
- The 7 All-Time Greatest Ideation Techniques[34]
- A Guide to Journalism and Design[35]
- Introduction to the Essential Ideation Techniques which are the Heart of Design Thinking[36]
- 10 Longtime Brainstorming Techniques that Still Work[37]
- 6 Types of Brainstorms that Help Create Awesome Ideas[38]
- Ideation – Learn More About Your Innate Talents from Gallup’s Clifton StrengthsFinder![39]
OPPORTUNITIES
Media Ideation Fellowship
Voqal.org offers a Media Ideation Fellowship for social entrepreneurs.[40] The technology accelerator is interested in founders who will “transform progressive politics or remedy a social inequity.”
National Grants and Competitions for Media Ventures
You’ll read more about other sources of nontraditional funding and resources in the Startup Funding chapter of this open textbook. Here is one crowdsourced list[41] of such opportunities.
Michelle Ferrier is an associate professor in the E.W. Scripps School of Journalism at Ohio University. She is the founder of Troll-Busters.com, an online pest control service for women journalists. Reach her on Twitter at @mediaghosts.
Leave feedback on this chapter.
- ”Stanford School Design Thinking Process," https://goo.gl/jua3VS ↵
- Faisal Hoque, ”Why Most Venture-Backed Companies Fail,” Fast Company, December 10, 2012, https://www.fastcompany.com/3003827/why-most-venture-backed-companies-fail. ↵
- FAQs About Copyright, United States Copyright Office, https://www.copyright.gov/help/faq/index.html. ↵
- Patent FAQs, United States Patent and Trademark Office, https://www.uspto.gov/help/patent-help. ↵
- Trademark FAQs, United States Patent and Trademark Office, https://www.uspto.gov/learning-and-resources/trademark-faqs. ↵
- Eric Michael, "What is Creativity?” https://www.ucf.edu/pegasus/what-is-creativity. ↵
- Jay Hathaway, “What is Gamergate, and Why? An Explainer for Non-Geeks,” Gawker, October 10, 2014, http://gawker.com/what-is-gamergate-and-why-an-explainer-for-non-geeks-1642909080. ↵
- Amy Webb, http://amywebb.io/. ↵
- Amy Webb, The Signals Are Talking. (New York: Public Affairs, 2016). ↵
- NMC Horizon Project, https://www.nmc.org/nmc-horizon. ↵
- https://www.nmc.org/nmc-horizon/ ↵
- ”Top 5 Technology Trends 2017,” Accenture, https://www.accenture.com/us-en/insight-disruptive-technology-trends-2017. ↵
- Pew Research Center, http://www.pewresearch.org/. ↵
- Innovating for People Handbook of Human-Centered Design Methods (Pittsburgh: LUMA Institute, 2012), https://www.amazon.com/Innovating-People-Handbook-Human-Centered-Methods/dp/0985750901. ↵
- LUMA Institute, http://www.luma-institute.com/. ↵
- Tony Deifell, ”The Big Thaw: Charting a New Future for Journalism,” The Media Consortium, http://www.thebigthaw.com/. ↵
- ”BBC News on Your Mobile,” BBC News, June 29, 2015, http://www.bbc.com/news/10628994. ↵
- Erick Schonfeld, "(Founder Stories) How Mike McCue Came Up With Flipboard: 'What If We Accidentally Deleted The Web.' TechCrunch, June 12, 2011, https://techcrunch.com/2011/06/12/founder-stories-mike-mccue-flipboard. ↵
- I developed the site over three years, building advertising revenue during that time. However, LocallyGrownNews.com was only sustainable as a side hustle, and a job opportunity in another state forced me to shutter the site. ↵
- ”The Value of Balancing Desirability, Feasibility, and Viability,” Crowd Favorite, https://crowdfavorite.com/the-value-of-balancing-desirability-feasibility-and-viability/. ↵
- "Innovating for People: Human-Centered Design Planning Cards," LUMA Institute, https://goo.gl/efaZc8. ↵
- ”Field Guide to Human-Centered Design,” IDEO.org, http://d1r3w4d5z5a88i.cloudfront.net/assets/guide/Field%20Guide%20to%20Human-Centered%20Design_IDEOorg_English-ee47a1ed4b91f3252115b83152828d7e.pdf. ↵
- "Ideation Method Mashup," IDEO.org, http://www.ideou.com/pages/ideation-method-mash-up. ↵
- "Human-Centered Design," IDEO.org, http://www.designkit.org/human-centered-design. ↵
- "LUMA Workplace," YouTube, https://www.youtube.com/watch?v=qDyElJ0xe2o. ↵
- "Explore Your Hunch," IDEO.org, http://www.designkit.org/methods/32. ↵
- Aha!, http://towknight.org/aha/ ↵
- "Top 5," IDEO.org, http://www.designkit.org/methods/15. ↵
- "Brainstorm Rules," IDEO.org, http://www.designkit.org/methods/28 ↵
- ”SWOT Analyis,” MindTools, https://www.mindtools.com/pages/article/newTMC_05.htm. ↵
- Peter Schmidt and Sarah Kim, “The Creativity Imperative in the Innovation and Entrepreneurship Curriculum: A Dilemma in the Scholarship of Teaching” Advances in Business-Related Scientific Research Conference 2014, https://goo.gl/rdsSdR. ↵
- Holger Berg, Vesa Taatila, and Christine Volkmann, "Fostering Creativity – a Holistic Framework for Teaching Creativity," Development and Learning in Organizations: An International Journal, http://www.emeraldinsight.com/doi/full/10.1108/14777281211272242. ↵
- "A Taxonomy of Innovation," Harvard Business Review, https://hbr.org/2014/01/a-taxonomy-of-innovation. ↵
- “The 7 All-Time Greatest Ideation Techniques,” Innovation Management, http://www.innovationmanagement.se/2013/05/30/the-7-all-time-greatest-ideation-techniques/. ↵
- "A Guide to Journalism and Design," Tow Center for Digital Journalism, http://towcenter.org/a-guide-to-journalism-and-design/. ↵
- Rikke Dam and Teo Siang, “Introduction to the Essential Ideation Techniques Which are the Heart of Design Thinking,” Interaction Design, https://www.interaction-design.org/literature/article/introduction-to-the-essential-ideation-techniques-which-are-the-heart-of-design-thinking. ↵
- John Boitnott, "10 Longtime Brainstorming Techniques that Still Work," Inc.com, http://www.inc.com/john-boitnott/10-longtime-brainstorming-techniques-that-still-work.html. ↵
- "6 Types of Brainstorms that Help Create Awesome Ideas," Pace, http://www.paceco.com/insights/strategy/brainstorm-techniques/. ↵
- "Ideation - Learn More About Your Innate Talents from Gallup's Clifton StrengthsFinder!" Gallup Strengths Center on YouTube, https://www.youtube.com/watch?v=55ZC1u42Xww. ↵
- "Media Ideation Fellowship," Voqal.org, http://voqal.org/initiatives/voqal-fund/media-ideation-fellowship/. ↵
- https://goo.gl/981PxS ↵


Case 4.2: Rain Shadow Meals on Wheels
Rain Shadow Meals on Wheels (i.e. “Rain Shadow”) prepares and delivers hot meals to senior citizens. Its fiscal year is January-December. At the end of fiscal year 2018, it had the following ending balances for its assets, liabilities, and net assets.
| ACCOUNT | FY 2018 |
| ENDING BALANCE | |
| Cash | $208,500 |
| Accounts Payable | $75,000 |
| Accounts Receivable | $50,000 |
| Pledges Receivable | $10,000 |
| Pre-Paid Expenses | $0 |
| Note Payable | $8,000 |
| Deferred Revenue | $1,000 |
| Inventory | $75,000 |
| Property Plant & Equipment | $100,000 |
| Long-Term Investments | $1,000,000 |
| Net Assets with Donor Restrictions | $1,004,500 |
| Wages Payable | $5,000 |
Using the worksheet below and the chart of accounts for the ending balances listed above, record these transactions for Rain Shadow during fiscal year 2019:
- On January 2, 2019, Rain Shadow purchased $100,000 of new food preparation equipment. It was paid with cash.
- On January 10, 2019, Rain Shadow paid $15,000 for a full year of insurance on its food preparation/distribution facility.
- On January 15, 2019, Rain Shadow paid $5,000 in wages employees earned in the final pay period of 2018.
- In November 2018, a local community foundation donated $2,500 for a nutrition education program that Rain Shadow agreed to deliver in early 2019. On February 1, 2019, Rain Shadow delivered that program. To deliver that program, it paid $2,000 to an outside consultant and used $500 of inventory.
- On April 1, 2019, Rain Shadow concluded its first quarter fundraising drive. It received $50,000 in cash donations and $100,000 in pledges. Historically, 90 percent of pledges have been collected.
- On July 12, 2019, Rain Shadow paid its suppliers and vendors $25,000.
- On July 15, 2019, Rain Shadow purchased inventory valued at $10,000 and received invoices from its suppliers.
- On September 1, 2019, a local wholesale food distributor donated $2,000 of supplies. Rain Shower used that food to prepare meals.
- On November 10, 2019, a local adult day services center paid Rain Shadow $5,000 for a nutrition education program. Rain Shadow will deliver that program in early 2020.
- On December 10, 2019, Rain Shadow’s investment manager reported that long-term investments are now valued at $1,050,000. Rain Shadow had received interest and dividend income from its investments of $35,000. All income from investments would be used to support general operations.
- Through December 31, 2019, Rain Shadow used $80,000 of labor. All wages were paid in cash.
- Depreciation expense totaling $20,000 was recorded on December 31, 2019.
Using the chart of accounts, the following Excel template file (https://bit.ly/3Pe3f5K) and transactions for the year ended December 31, 2019, to prepare the Statement of Financial Position and Statement of Activities for the year ended December 31, 2019.


10 Self Exploration Through Collage
“Images have a way of bypassing the chatter of our logical minds and nudging our deep soul wisdom.” –Soul Collage
Purpose:
Artistic expression can be intimidating to people who feel insecure about their creative abilities. Playing with collage materials breaks through those inhibitions as participants are using colours, images and words from magazines, posters, cards, photos or other printed materials to express their inner world. The purpose of collaging is to explore images and colours that express participants’ emotions, dreams and inner worlds.
Learning Objectives
Particpants will:
- Express emotions, fears, goals or dreams using images from print media or photos from their lives.
- Share with each other in small groups why they chose these images and what they mean to the creator.
Collage Cards:
This activity is loosely adapted from the “Soul Collage” process created by therapist Seena Frost. For more information about her formal process of creating soul collage decks of cards, refer to her book and website: soulcollage.com
Collage Identity Cards Activity Directions:
- Reflection: Hand out 5 by 7 index cards or cut cardstock paper to the size of large postcards. Lead individual or group in a short meditation where they explore the question “Who am I?” The following questions might help them access the visual imagery of their experience:
Exploration questions:
- What thoughts and emotions arise as you contemplate the question: “Who am I in this very moment?’
- Pay attention to the energy in your body and mind. If this energy was a colour, what colour would it be?
- Notice if there are thoughts or memories of your past or worries about your future. When they arise, gently notice them and come back to your present experience. Who am I right now? What do I hear, feel, experience in this moment?
- Are there any images that come to mind that represent how you feel right now. These might be colours, shapes, creatures, plants or anything else that is a symbol or your current experience.
2. Find Materials: Ask the group or individual to open their eyes and move to the table where the collage materials are laid out. Ask people to stay silent through this process so they are accessing the non-verbal parts of their brain.
3. Create Collage: Allow 20 to 30 minutes for participants to cut out images and glue them to their cards.
4. Write Reflections: As people complete their cards, ask them to turn them over and write on the back side of the card their reflection on what the card shows about their personal identity in this moment.
5. Small Group Discussion: In a class or group setting, have participants form groups of 3 – 4 and share their cards and describe their experience of exploring their identity through collage. Participants could also ask their group mates what they see in the card. What does it show them about the collage artist’s identity?
6. Full Group Discussion: Bring the full group back together and debrief with some of the following questions:
- What did you learn about yourself while creating your collage card?
- What did you learn about your group mates when sharing your cards?
- How do you feel about expressing yourself through art?
- What is it different about expressing yourself through art or through language?
- In what ways do you think collage is like a metaphor for life?
Reflections written on back of the card completing the sentence stem “I am ________ “
(the collage is like a dream revealing aspects of the collage artist’s present being)
“I am reaching for connection. I am the minaret and the Buddha who teach of generosity, integrity and peace. I am the tiny human held by the parachute wondering about my purpose in this life and wanting perspective. I want to look down on the ephemeral flowers and bubbles and flowing horses and feel gratitude for the small moments in life. I am the one who seeks beauty and some kind of pattern in the randomness of life.”
Extension Activities with Collage Cards
- Storytelling: With a small group you can use the collaged cards as a story telling activity. Place people’s personal collage cards face down in the middle of the group and mix them up so no one knows whose card they will be picking. Ask one person to pick a random card, reflect on it and start a story based on what they see in the card. The next person in the circle picks another card and continues the story until all the cards are used. Ask the group what it was like to have their personal collage spoken about by another person and how they felt about their card’s role in the group story.
- Writing: Combine collage with a writing activity. The following journal spread combines writing about an identified strength from a Clifton Strengths Assessment with collage images that help explore the personal meaning of this strength in the participant’s life.
- Neurographic Art: Neurographic art invites people to consider something in their life where they are seeking clarity. They then spend 3 seconds scribbling looping lines on the page as they consider their issue. After that, they round the corners of the sharp lines and fill in spaces with colours. As they are doodling, they are contemplating possible ways of handling an issue or dilemma. The theory is that the art frees up the mind to find novel approaches to personal conundrums. These neurographic pieces can form the center of a mandala where collage can be added for complementary images and meanings.


Learning Objectives
By the end of this section, you will be able to:
Describe the microscopic and gross anatomical structures of bones
- Identify the gross anatomical features of a bone
- Describe the histology of bone tissue, including the function of bone cells and matrix
- Compare and contrast compact and spongy bone
- Identify the structures that compose compact and spongy bone
- Describe how bones are nourished and innervated
- function?
Bone tissue (osseous tissue) differs greatly from other tissues in the body. Bone is hard and many of its functions depend on that characteristic hardness. Later discussions in this chapter will show that bone is also dynamic in that its shape adjusts to accommodate stresses. This section will examine the gross anatomy of bone first and then move on to its histology.
Gross Anatomy of Bones
A long bone has two main regions: the diaphysis and the epiphysis (Figure 6.3.1). The diaphysis is the hollow, tubular shaft that runs between the proximal and distal ends of the bone. Inside the diaphysis is the medullary cavity, which is filled with yellow bone marrow in an adult. The outer walls of the diaphysis (cortex, cortical bone) are composed of dense and hard compact bone, a form of osseous tissue.
The wider section at each end of the bone is called the epiphysis (plural = epiphyses), which is filled internally with spongy bone, another type of osseous tissue. Red bone marrow fills the spaces between the spongy bone in some long bones. Each epiphysis meets the diaphysis at the metaphysis. During growth, the metaphysis contains the epiphyseal plate, the site of long bone elongation described later in the chapter. When the bone stops growing in early adulthood (approximately 18–21 years), the epiphyseal plate becomes an epiphyseal line seen in the figure.
Lining the inside of the bone adjacent to the medullary cavity is a layer of bone cells called the endosteum (endo- = “inside”; osteo- = “bone”). These bone cells (described later) cause the bone to grow, repair, and remodel throughout life. On the outside of bones there is another layer of cells that grow, repair and remodel bone as well. These cells are part of the outer double layered structure called the periosteum (peri– = “around” or “surrounding”). The cellular layer is adjacent to the cortical bone and is covered by an outer fibrous layer of dense irregular connective tissue (see Figure 6.3.4a). The periosteum also contains blood vessels, nerves, and lymphatic vessels that nourish compact bone. Tendons and ligaments attach to bones at the periosteum. The periosteum covers the entire outer surface except where the epiphyses meet other bones to form joints (Figure 6.3.2). In this region, the epiphyses are covered with articular cartilage, a thin layer of hyaline cartilage that reduces friction and acts as a shock absorber.
Flat bones, like those of the cranium, consist of a layer of diploë (spongy bone), covered on either side by a layer of compact bone (Figure 6.3.3). The two layers of compact bone and the interior spongy bone work together to protect the internal organs. If the outer layer of a cranial bone fractures, the brain is still protected by the intact inner layer.
Osseous Tissue: Bone Matrix and Cells
Bone Cells
Although bone cells compose less than 2% of the bone mass, they are crucial to the function of bones. Four types of cells are found within bone tissue: osteoblasts, osteocytes, osteogenic cells, and osteoclasts (Figure 6.3.5).
The osteoblast is the bone cell responsible for forming new bone and is found in the growing portions of bone, including the endosteum and the cellular layer of the periosteum. Osteoblasts, which do not divide, synthesize and secrete the collagen matrix and other proteins. As the secreted matrix surrounding the osteoblast calcifies, the osteoblast become trapped within it; as a result, it changes in structure and becomes an osteocyte, the primary cell of mature bone and the most common type of bone cell. Each osteocyte is located in a small cavity in the bone tissue called a lacuna (lacunae for plural). Osteocytes maintain the mineral concentration of the matrix via the secretion of enzymes. Like osteoblasts, osteocytes lack mitotic activity. They can communicate with each other and receive nutrients via long cytoplasmic processes that extend through canaliculi (singular = canaliculus), channels within the bone matrix. Osteocytes are connected to one another within the canaliculi via gap junctions.
If osteoblasts and osteocytes are incapable of mitosis, then how are they replenished when old ones die? The answer lies in the properties of a third category of bone cells—the osteogenic (osteoprogenitor) cell. These osteogenic cells are undifferentiated with high mitotic activity and they are the only bone cells that divide. Immature osteogenic cells are found in the cellular layer of the periosteum and the endosteum. They differentiate and develop into osteoblasts.
The dynamic nature of bone means that new tissue is constantly formed, and old, injured, or unnecessary bone is dissolved for repair or for calcium release. The cells responsible for bone resorption, or breakdown, are the osteoclasts. These multinucleated cells originate from monocytes and macrophages, two types of white blood cells, not from osteogenic cells. Osteoclasts are continually breaking down old bone while osteoblasts are continually forming new bone. The ongoing balance between osteoblasts and osteoclasts is responsible for the constant but subtle reshaping of bone. Table 6.3 reviews the bone cells, their functions, and locations.
| Bone Cells (Table 6.3) | ||
|---|---|---|
| Cell type | Function | Location |
| Osteogenic cells | Develop into osteoblasts | Endosteum, cellular layer of the periosteum |
| Osteoblasts | Bone formation | Endosteum, cellular layer of the periosteum, growing portions of bone |
| Osteocytes | Maintain mineral concentration of matrix | Entrapped in matrix |
| Osteoclasts | Bone resorption | Endosteum, cellular layer of the periosteum, at sites of old, injured, or unneeded bone |
Compact and Spongy Bone
Most bones contain compact and spongy osseous tissue, but their distribution and concentration vary based on the bone’s overall function. Although compact and spongy bone are made of the same matrix materials and cells, they are different in how they are organized. Compact bone is dense so that it can withstand compressive forces, while spongy bone (also called cancellous bone) has open spaces and is supportive, but also lightweight and can be readily remodeled to accommodate changing body needs.
Compact Bone
Compact bone is the denser, stronger of the two types of osseous tissue (Figure 6.3.6). It makes up the outer cortex of all bones and is in immediate contact with the periosteum. In long bones, as you move from the outer cortical compact bone to the inner medullary cavity, the bone transitions to spongy bone.
If you look at compact bone under the microscope, you will observe a highly organized arrangement of concentric circles that look like tree trunks. Each group of concentric circles (each “tree”) makes up the microscopic structural unit of compact bone called an osteon (this is also called a Haversian system). Each ring of the osteon is made of collagen and calcified matrix and is called a lamella (plural = lamellae). The collagen fibers of adjacent lamallae run at perpendicular angles to each other, allowing osteons to resist twisting forces in multiple directions (see figure 6.34a). Running down the center of each osteon is the central canal, or Haversian canal, which contains blood vessels, nerves, and lymphatic vessels. These vessels and nerves branch off at right angles through a perforating canal, also known as Volkmann’s canals, to extend to the periosteum and endosteum. The endosteum also lines each central canal, allowing osteons to be removed, remodeled and rebuilt over time.
The osteocytes are trapped within their lacuane, found at the borders of adjacent lamellae. As described earlier, canaliculi connect with the canaliculi of other lacunae and eventually with the central canal. This system allows nutrients to be transported to the osteocytes and wastes to be removed from them despite the impervious calcified matrix.
Spongy (Cancellous) Bone
Like compact bone, spongy bone, also known as cancellous bone, contains osteocytes housed in lacunae, but they are not arranged in concentric circles. Instead, the lacunae and osteocytes are found in a lattice-like network of matrix spikes called trabeculae (singular = trabecula) (Figure 6.3.8). The trabeculae are covered by the endosteum, which can readily remodel them. The trabeculae may appear to be a random network, but each trabecula forms along lines of stress to direct forces out to the more solid compact bone providing strength to the bone. Spongy bone provides balance to the dense and heavy compact bone by making bones lighter so that muscles can move them more easily. In addition, the spaces in some spongy bones contain red bone marrow, protected by the trabeculae, where hematopoiesis occurs.
Paget’s disease usually occurs in adults over age 40. It is a disorder of the bone remodeling process that begins with overactive osteoclasts. This means more bone is resorbed than is laid down. The osteoblasts try to compensate but the new bone they lay down is weak and brittle and therefore prone to fracture.
While some people with Paget’s disease have no symptoms, others experience pain, bone fractures, and bone deformities (Figure 6.3.9). Bones of the pelvis, skull, spine, and legs are the most commonly affected. When occurring in the skull, Paget’s disease can cause headaches and hearing loss.
What causes the osteoclasts to become overactive? The answer is still unknown, but hereditary factors seem to play a role. Some scientists believe Paget’s disease is due to an as-yet-unidentified virus.
Paget’s disease is diagnosed via imaging studies and lab tests. X-rays may show bone deformities or areas of bone resorption. Bone scans are also useful. In these studies, a dye containing a radioactive ion is injected into the body. Areas of bone resorption have an affinity for the ion, so they will light up on the scan if the ions are absorbed. In addition, blood levels of an enzyme called alkaline phosphatase are typically elevated in people with Paget’s disease. Bisphosphonates, drugs that decrease the activity of osteoclasts, are often used in the treatment of Paget’s disease.
Blood and Nerve Supply
The spongy bone and medullary cavity receive nourishment from arteries that pass through the compact bone. The arteries enter through the nutrient foramen (plural = foramina), small openings in the diaphysis (Figure 6.3.10). The osteocytes in spongy bone are nourished by blood vessels of the periosteum that penetrate spongy bone and blood that circulates in the marrow cavities. As the blood passes through the marrow cavities, it is collected by veins, which then pass out of the bone through the foramina.
In addition to the blood vessels, nerves follow the same paths into the bone where they tend to concentrate in the more metabolically active regions of the bone. The nerves sense pain, and it appears the nerves also play roles in regulating blood supplies and in bone growth, hence their concentrations in metabolically active sites of the bone.
External Website
Watch this video to see the microscopic features of a bone.
Chapter Review
A hollow medullary cavity filled with yellow marrow runs the length of the diaphysis of a long bone. The walls of the diaphysis are compact bone. The epiphyses, which are wider sections at each end of a long bone, are filled with spongy bone and red marrow. The epiphyseal plate, a layer of hyaline cartilage, is replaced by osseous tissue as the organ grows in length. The medullary cavity has a delicate membranous lining called the endosteum. The outer surface of bone, except in regions covered with articular cartilage, is covered with a fibrous membrane called the periosteum. Flat bones consist of two layers of compact bone surrounding a layer of spongy bone. Bone markings depend on the function and location of bones. Articulations are places where two bones meet. Projections stick out from the surface of the bone and provide attachment points for tendons and ligaments. Holes are openings or depressions in the bones.
Bone matrix consists of collagen fibers and organic ground substance, primarily hydroxyapatite formed from calcium salts. Osteogenic cells develop into osteoblasts. Osteoblasts are cells that make new bone. They become osteocytes, the cells of mature bone, when they get trapped in the matrix. Osteoclasts engage in bone resorption. Compact bone is dense and composed of osteons, while spongy bone is less dense and made up of trabeculae. Blood vessels and nerves enter the bone through the nutrient foramina to nourish and innervate bones.
Review Questions
Critical Thinking Questions
1. If the articular cartilage at the end of one of your long bones were to degenerate, what symptoms do you think you would experience? Why?
2. In what ways is the structural makeup of compact and spongy bone well suited to their respective functions?
Glossary
- articular cartilage
- thin layer of cartilage covering an epiphysis; reduces friction and acts as a shock absorber
- articulation
- where two bone surfaces meet
- canaliculi
- (singular = canaliculus) channels within the bone matrix that house one of an osteocyte’s many cytoplasmic extensions that it uses to communicate and receive nutrients
- central canal
- longitudinal channel in the center of each osteon; contains blood vessels, nerves, and lymphatic vessels; also known as the Haversian canal
- compact bone
- dense osseous tissue that can withstand compressive forces
- diaphysis
- tubular shaft that runs between the proximal and distal ends of a long bone
- diploë
- layer of spongy bone, that is sandwiched between two the layers of compact bone found in flat bones
- endosteum
- delicate membranous lining of a bone’s medullary cavity
- epiphyseal plate
- (also, growth plate) sheet of hyaline cartilage in the metaphysis of an immature bone; replaced by bone tissue as the organ grows in length
- epiphysis
- wide section at each end of a long bone; filled with spongy bone and red marrow
- hole
- opening or depression in a bone
- lacunae
- (singular = lacuna) spaces in a bone that house an osteocyte
- medullary cavity
- hollow region of the diaphysis; filled with yellow marrow
- nutrient foramen
- small opening in the middle of the external surface of the diaphysis, through which an artery enters the bone to provide nourishment
- osteoblast
- cell responsible for forming new bone
- osteoclast
- cell responsible for resorbing bone
- osteocyte
- primary cell in mature bone; responsible for maintaining the matrix
- osteogenic cell
- undifferentiated cell with high mitotic activity; the only bone cells that divide; they differentiate and develop into osteoblasts
- osteon
- (also, Haversian system) basic structural unit of compact bone; made of concentric layers of calcified matrix
- perforating canal
- (also, Volkmann’s canal) channel that branches off from the central canal and houses vessels and nerves that extend to the periosteum and endosteum
- periosteum
- fibrous membrane covering the outer surface of bone and continuous with ligaments
- projection
- bone markings where part of the surface sticks out above the rest of the surface, where tendons and ligaments attach
- spongy bone
- (also, cancellous bone) trabeculated osseous tissue that supports shifts in weight distribution
- trabeculae
- (singular = trabecula) spikes or sections of the lattice-like matrix in spongy bone
Solutions
Answers for Critical Thinking Questions
- If the articular cartilage at the end of one of your long bones were to deteriorate, which is actually what happens in osteoarthritis, you would experience joint pain at the end of that bone and limitation of motion at that joint because there would be no cartilage to reduce friction between adjacent bones and there would be no cartilage to act as a shock absorber.
- The densely packed concentric rings of matrix in compact bone are ideal for resisting compressive forces, which is the function of compact bone. The open spaces of the trabeculated network of spongy bone allow spongy bone to support shifts in weight distribution, which is the function of spongy bone.
Bone Markings
Define and list examples of bone markings
The surface features of bones vary considerably, depending on the function and location in the body. Table 6.2 describes the bone markings, which are illustrated in (Figure 6.3.4). There are three general classes of bone markings: (1) articulations, (2) projections, and (3) holes. As the name implies, an articulation is where two bone surfaces come together (articulus = “joint”). These surfaces tend to conform to one another, such as one being rounded and the other cupped, to facilitate the function of the articulation. A projection is an area of a bone that projects above the surface of the bone. These are the attachment points for tendons and ligaments. In general, their size and shape is an indication of the forces exerted through the attachment to the bone. A hole is an opening or groove in the bone that allows blood vessels and nerves to enter the bone. As with the other markings, their size and shape reflect the size of the vessels and nerves that penetrate the bone at these points.
| Bone Markings (Table 6.2) | ||
|---|---|---|
| Marking | Description | Example |
| Articulations | Where two bones meet | Knee joint |
| Head | Prominent rounded surface | Head of femur |
| Facet | Flat surface | Vertebrae |
| Condyle | Rounded surface | Occipital condyles |
| Projections | Raised markings | Spinous process of the vertebrae |
| Protuberance | Protruding | Chin |
| Process | Prominence feature | Transverse process of vertebra |
| Spine | Sharp process | Ischial spine |
| Tubercle | Small, rounded process | Tubercle of humerus |
| Tuberosity | Rough surface | Deltoid tuberosity |
| Line | Slight, elongated ridge | Temporal lines of the parietal bones |
| Crest | Ridge | Iliac crest |
| Holes | Holes and depressions | Foramen (holes through which blood vessels can pass through) |
| Fossa | Elongated basin | Mandibular fossa |
| Fovea | Small pit | Fovea capitis on the head of the femur |
| Sulcus | Groove | Sigmoid sulcus of the temporal bones |
| Canal | Passage in bone | Auditory canal |
| Fissure | Slit through bone | Auricular fissure |
| Foramen | Hole through bone | Foramen magnum in the occipital bone |
| Meatus | Opening into canal | External auditory meatus |
| Sinus | Air-filled space in bone | Nasal sinus |
This work, Anatomy & Physiology, is adapted from Anatomy & Physiology by OpenStax, licensed under CC BY. This edition, with revised content and artwork, is licensed under CC BY-SA except where otherwise noted.
Images, from Anatomy & Physiology by OpenStax, are licensed under CC BY except where otherwise noted.
Access the original for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction.


33
Adverbs
Adverbs in Greek function much as they do in English; namely, they provide additional information about a verb, adjective, or other adverb. Most often, they indicate manner, time, intensity, quantity, or place. In this lesson, we discuss adverbs that are formed from adjectives.
Formation
The most common ending for an adverb is –ως. This ending corresponds almost exactly to the –ly ending in English. Adverbs do not decline.
To form this type of adverb, start with the MASCULINE GENITIVE PLURAL of the ADJECTIVE and substitute –ς for the final –ν (S 343). (Τhe adverb does not, in fact, derive from the genitive plural, but this method provides a convenient way to determine the form of the adverb.) The ACCENT remains as it was on the genitive plural.
For example:
| Adjective | Genitive Plural | Adverb |
| ἀληθής ἀληθές | ἀληθῶν | ἀληθῶς |
| ἡδύς ἡδεῖα ἡδύ | ἡδέων | ἡδέως |
| κακός –ή –όν | κακῶν | κακῶς |
| ὅλος -η -ον | ὅλων | ὅλως |
Vocabulary
Greek adverbs derived from adjectives are not normally listed in a vocabulary or lexicon, since they form regularly and have predictable meanings. If an adverb has a more specialized meaning or distinct form, however, it is listed. Note, for example, the following common adverbs:
- ἄλλως otherwise
- ἅπλως singly, in one way, simply
- ἴσως equally, probably, perhaps
- ὅμως likewise, equally
- οὕτω/οὕτως in this way, thus
- πάντως altogether, in all ways, at any rate
- πάνυ altogether, entirely, certainly
- τὸ πρῶτον first
- πῶς in what way? how?
- πως (enclitic) in any way
- ὕστερον afterwards
- ὧδε thus, in this way; here
- ὡς as
- ὥσπερ just as, as if
Numbers
Cardinal Numbers
Ancient Greek normally writes out cardinal numbers. The numbers one, two, three and four decline, most in the 3rd declension. The numbers from 5 to 199 do not decline.
- εἷς, μία, ἕν one
- δύο two
- τρεῖς, τρία three
- τέτταρες, τέτταρα four
We have already learned how to inflect the number one. To review:
εἷς μία ἕν one (S 349; GPH p. 37)
| M | F | N | |
| Nominative | εἷς | μία | ἕν |
| Genitive | ἑνός | μιᾶς | ἑνός |
| Dative | ἑνί | μιᾷ | ἑνί |
| Accusative | ἕνα | μίαν | ἕν |
δύο two (S 349; GPH p. 37)
| M/F/N | |
| Nominative | δύο |
| Genitive | δυοῖν |
| Dative | δυοῖν |
| Accusative | δύο |
τρεῖς, τρία three (S 349; GPH p. 38)
| M/F | N | |
| Nominative | τρεῖς | τρία |
| Genitive | τριῶν | τριῶν |
| Dative | τρισί | τρισί |
| Accusative | τρεῖς | τρία |
τέτταρες, τέτταρα four (S 349; GPH p. 38)
| M/F | N | |
| Nominative | τέτταρες | τέτταρα |
| Genitive | τεττάρων | τεττάρων |
| Dative | τέτταρσι | τέτταρσι |
| Accusative | τέτταρας | τέτταρα |
The cardinal numbers 5-29 (S 347)
| five: πέντε | fourteen: τέτταρες καὶ δέκα |
| six: ἕξ | fifteen: πεντεκαίδεκα |
| seven: ἑπτά | sixteen: ἑκκαίδεκα |
| eight: ὀκτώ | seventeen: ἑπτακαίδεκα |
| nine: ἐννέα | eighteen: ὀκτωκαίδεκα |
| ten: δέκα | nineteen: ἐννεακαίδεκα |
| eleven: ἕνδεκα | twenty: εἴκοσι |
| twelve: δώδεκα | twenty one: εἷς καὶ εἴκοσι |
| thirteen: τρεῖς καὶ δέκα | twenty two: δύο καὶ εἴκοσι κτλ |
– κοντα indicates the tens (-ty)
| thirty: τριάκοντα | seventy: ἑβδομήκοντα |
| forty: τετταράκοντα | eighty: ὀγδοήκοντα |
| fifty: πεντήκοντα | ninety: ἐνενήκοντα |
| sixty: ἑξήκοντα | one hundred: ἑκατόν |
– κόσιοι indicates the hundreds. Note that the numbers two hundred and higher decline as 1st and 2nd declension adjectives.
| two hundred: διακόσιοι –αι –α | thousand: χίλιοι –αι –α |
| three hundred: τριακόσιοι –αι –α | two thousand: δισχίλιοι –αι –α |
| four hundred: τετρακόσιοι –αι –α | three thousand: τρισχίλιοι –αι –α |
| five hundred: πεντακόσιοι –αι –α | ten thousand: μύριοι –αι –α |
| six hundred: ἑξακόσιοι –αι –α | twenty thousand: δισμύριοι –αι –α |
| seven hundred: ἑπτακόσιοι –αι –α | = δύο μυριάδες |
| eight hundred: ὀκτακόσιοι –αι –α | hundred thousand: δεκακισμύριοι –αι –α |
| nine hundred: ἐνακόσιοι –αι –α | hundred million: μυριάκις μύριοι –αι –α |
Greek usually expresses written compound numbers above 20 (21, 22…) in one of two ways:
- placing the smaller number first, followed by καί and the larger number
- εἷς καὶ εἴκοσι
- placing the larger number first, followed by the smaller number. In this order, καί is optional.
- εἴκοσι καὶ εἷς
- εἴκοσι εἷς
Numeral Notation
In the Classical period, inscriptions show the following numerals. This system is called ACROPHONIC, i.e., some of the numbers are represented by the first letter of the word for that number (S 348A). Note, for example, a version of the Π = πέντε; Δ = δέκα; Η =ἑκατόν (Η in an earlier alphabet was the letter representing a rough breathing, and so was the first letter of the older form hεκατόν); Χ = χίλιοι; and Μ = μύριοι.
Note also the compound signs. In these cases, multiply the numbers that comprise the compound.
After the 2nd c. B.C., ALPHABETIC NUMERALS replace the acrophonic system (S 347).
Ordinal Numbers
Ancient Greek normally writes out ordinal numbers. Note that ordinals decline as regular 1st and 2nd declension adjectives (S 347).
| first: πρῶτος –η –ον | twelfth: δωδέκατος –η –ον |
| second: δεύτερος –α –ον | thirteenth: τρίτος καὶ δέκατος κτλ |
| third: τρίτος –η –ον | twentieth: εἰκοστός –ή –όν |
| fourth: τέταρτος –η –ον | thirtieth: τριακοστός –ή –όν |
| fifth: πέμπτος –η –ον | fortieth: τετταρακοστός –ή –όν |
| sixth: ἕκτος –η –ον | fiftieth: πεντηκοστός –ή –όν |
| seventh: ἕβδομος –η –ον | sixtieth: ἑξηκοστός –ή –όν |
| eighth: ὄγδοος –η –ον | seventieth: ἑβδομηκοστός –ή –όν |
| ninth: ἔνατος –η –ον | eightieth: ὀγδοηκοστός –ή –όν |
| tenth: δέκατος –η –ον | ninetieth: ἐνενηκοστός –ή –όν |
| eleventh: ἐνδέκατος –η –ον | hundredth: ἑκατοστός –ή –όν |
Number Adverbs
With the exception of ἅπαξ once, δίς twice, and τρίς thrice, Greek normally adds –κις to a cardinal number to make numeral adverbs (S 347).
For example:
- ἅπαξ once
- δίς twice
- τρίς thrice, three times
- τετράκις four times
- πεντάκις five times
- ἑξάκις six times
- δεκάκις ten times
With number adverbs in hand, now we can do some math!
- ἑκκαίδεκα καὶ τέτταρά εἰσιν εἴκοσι
- sixteen plus (and) four equals (are) twenty
- τὰ πεντάκις δέκα ἐστὶ πεντήκοντα
- five times ten (or: ten five times) equals (is) fifty
– τὸ τέλος –
Paradigms, Key Terms and Concepts
- Chapter Paradigms
- ADVERBS FORMED FROM ADJECTIVES
- CARDINAL NUMBERS
- ACROPHONIC NUMERALS
- ALPHABETIC NUMERALS
- ORDINAL NUMBERS
- NUMBER ADVERBS
Vocabulary List 1
Adverbs
- ἄλλως otherwise
- ἅπλως singly, in one way, simply
- ἴσως equally, probably, perhaps
- ὅμως likewise, equally
- οὕτω/οὕτως in this way, thus
- πάντως altogether, in all ways, at any rate
- πάνυ altogether, entirely, certainly
- τὸ πρῶτον first
- πῶς in what way? how?
- πως (enclitic) in any way
- ὕστερον afterwards
- ὧδε thus, in this way; here
- ὡς as
- ὥσπερ just as, as if
- ἅπαξ once
- δίς twice
- τρίς thrice
Vocabulary List 2
Cardinal Numbers
- εἷς μία ἕν one
- δύο two
- τρεῖς τρία three
- τέτταρες τέτταρα four
- πέντε five
- ἕξ six
- ἑπτά seven
- ὀκτώ eight
- ἐννέα nine
- δέκα ten
- εἴκοσι twenty
- τριάκοντα thirty
- ἑκατόν one hundred
- μύριοι –αι –α ten thousand
- μυρίος -α -ον countless
- μυριάς -άδος ἡ ten thousand, countless
Ordinal Numbers
- πρῶτος –η –ον first
- δεύτερος –α –ον second
- τρίτος –η –ον third
- τέταρτος –η –ον fourth
- πέμπτος –η –ον fifth
- ἕκτος –η –ον sixth
- ἕβδομος –η –ον seventh
- ὄγδοος –η –ον eighth
- ἔνατος –η –ον ninth
- δέκατος –η –ον tenth
- εἰκοστός –ή –όν twentieth
- τριακοστός –ή –όν thirtieth
- ἑκατοστός –ή –όν hundredth
Exercises
Ι. Decline in all cases and numbers the following cardinal numbers.
- εἷς μία ἕν
- δύο
- τρεῖς τρία
- τέτταρες τέτταρα
ΙΙ. Supply, in Greek, the answers to the following math problems:
e.g.: ἑκκαίδεκα καὶ τέτταρά εἰσιν εἴκοσι = sixteen plus (and) four equals (are) twenty
- τρεῖς καὶ ἕξ εἰσι ________________
- δέκα καὶ δέκα εἰσὶ ________________
- ἕνδεκα καὶ δώδεκά εἰσι ________________
- τὰ ἑξάκις πέντε ἐστὶ ________________
- τὰ δεκάκις ἑκατόν ἐστι ________________
- τὰ πεντάκις _______________ ἐστι τετταράκοντα
- δὶς _______________ ἢ τρὶς _______________ ἢ τετράκις ______________ ἢ ἑξάκις _______________ ἐστὶ τὰ δώδεκα
Readings
κατὰ Λουκᾶν 12:49-56: AGE Ch. 33a.
IG i3 421, a sale of slaves: AGE Ch. 33b. (For a photo of this inscription, click here.)


Observational Learning
Not all forms of learning are accounted for entirely by classical and operant conditioning.  The game looks fun, but it is new and unfamiliar. Rather than joining the game immediately, the child opts to sit back and watch the other children play a round or two. Observing the others, the child takes note of the ways in which they behave while playing the game. By watching the behavior of the other kids, the child can figure out the rules of the game and even some strategies for doing well at the game. This is called observational learning.
Children observing a social model (an experienced chess player) to learn the rules and strategies of the game of chess. [Image: David R. Tribble, https://goo.gl/nWsgxI, CC BY-SA 3.0, https://goo.gl/ uhHola]
Observational learning is a component of Albert Bandura’s Social Learning Theory (Bandura, 1977), which posits that individuals can learn novel responses via observation of key others’ behaviors. Observational learning does not necessarily require reinforcement, but instead hinges on the presence of others, referred to as social models. Social models are typically of higher status or authority compared to the observer, examples of which include parents, teachers, and police officers. In the example above, the children who already know how to play the game could be thought of as being authorities—and are therefore social models—even though they are the same age as the observer. By observing how the social models behave, an individual is able to learn how to act in a certain situation. Other examples of observational learning might include a child learning to place her napkin in her lap by watching her parents at the dinner table, or a customer learning where to find the ketchup and mustard after observing other customers at a hot dog stand.
Bandura theorizes that the observational learning process consists of four parts. The first is attention—as, quite simply, one must pay attention to what s/he is observing in order to learn. The second part is retention: to learn one must be able to retain the behavior s/he is observing in memory.The third part of observational learning, initiation, acknowledges that the learner must be able to execute (or initiate) the learned behavior. Lastly, the observer must possess the motivation to engage in observational learning. In our vignette, the child must want to learn how to play the game in order to properly engage in observational learning.
Researchers have conducted countless experiments designed to explore observational learning, the most famous of which is Albert Bandura’s “Bobo doll experiment.”
In this experiment (Bandura, Ross & Ross 1961), Bandura had children individually observe an adult social model interact with a clown doll (“Bobo”). For one group of children, the adult interacted aggressively with Bobo: punching it, kicking it, throwing it, and even hitting it in the face with a toy mallet. Another group of children watched the adult interact with other toys, displaying no aggression toward Bobo. In both instances the adult left and the children were allowed to interact with Bobo on their own. Bandura found that children exposed to the aggressive social model were significantly more likely to behave aggressively toward Bobo, hitting and kicking him, compared to those exposed to the non-aggressive model. The researchers concluded that the children in the aggressive group used their observations of the adult social model’s behavior to determine that aggressive behavior toward Bobo was acceptable.
While reinforcement was not required to elicit the children’s behavior in Bandura’s first experiment, it is important to acknowledge that consequences do play a role within observational learning. A future adaptation of this study (Bandura, Ross, & Ross, 1963) demonstrated that children in the aggression group showed less aggressive behavior if they witnessed the adult model receive punishment for aggressing against Bobo. Bandura referred to this process as vicarious reinforcement, as the children did not experience the reinforcement or punishment directly, yet were still influenced by observing it.
Bobo [Image: © Sémhur / Wikimedia Commons / CC-BY-SA-3.0 (or Free Art License), https://goo.gl/uhHola]


Chapter 16 Oscillatory Motion and Waves
16.9 Waves
Summary
- State the characteristics of a wave.
- Calculate the velocity of wave propagation.
What do we mean when we say something is a wave? The most intuitive and easiest wave to imagine is the familiar water wave. More precisely, a wave is a disturbance that propagates, or moves from the place it was created. For water waves, the disturbance is in the surface of the water, perhaps created by a rock thrown into a pond or by a swimmer splashing the surface repeatedly. For sound waves, the disturbance is a change in air pressure, perhaps created by the oscillating cone inside a speaker. For earthquakes, there are several types of disturbances, including disturbance of Earth’s surface and pressure disturbances under the surface. Even radio waves are most easily understood using an analogy with water waves. Visualizing water waves is useful because there is more to it than just a mental image. Water waves exhibit characteristics common to all waves, such as amplitude, period, frequency and energy. All wave characteristics can be described by a small set of underlying principles.
A wave is a disturbance that propagates, or moves from the place it was created. The simplest waves repeat themselves for several cycles and are associated with simple harmonic motion. Let us start by considering the simplified water wave in Figure 2. The wave is an up and down disturbance of the water surface. It causes a sea gull to move up and down in simple harmonic motion as the wave crests and troughs (peaks and valleys) pass under the bird. The time for one complete up and down motion is the wave’s period [latex]{T}.[/latex] The wave’s frequency is [latex]{f=1/T},[/latex] as usual. The wave itself moves to the right in the figure. This movement of the wave is actually the disturbance moving to the right, not the water itself (or the bird would move to the right). We define wave velocity [latex]{v_{\text{w}}}[/latex] to be the speed at which the disturbance moves. Wave velocity is sometimes also called the propagation velocity or propagation speed, because the disturbance propagates from one location to another.
MISCONCEPTION ALERT
Many people think that water waves push water from one direction to another. In fact, the particles of water tend to stay in one location, save for moving up and down due to the energy in the wave. The energy moves forward through the water, but the water stays in one place. If you feel yourself pushed in an ocean, what you feel is the energy of the wave, not a rush of water.
The water wave in the figure also has a length associated with it, called its wavelength [latex]{\lambda},[/latex] the distance between adjacent identical parts of a wave. ( [latex]{\lambda}[/latex] is the distance parallel to the direction of propagation.) The speed of propagation [latex]{v_{\text{w}}}[/latex] is the distance the wave travels in a given time, which is one wavelength in the time of one period. In equation form, that is
or
This fundamental relationship holds for all types of waves. For water waves, [latex]{v_{\text{w}}}[/latex] is the speed of a surface wave; for sound, [latex]{v_{\text{w}}}[/latex] is the speed of sound; and for visible light, [latex]{v_{\text{w}}}[/latex] is the speed of light, for example.
TAKE-HOME EXPERIMENT: WAVES IN A BOWL
Fill a large bowl or basin with water and wait for the water to settle so there are no ripples. Gently drop a cork into the middle of the bowl. Estimate the wavelength and period of oscillation of the water wave that propagates away from the cork. Remove the cork from the bowl and wait for the water to settle again. Gently drop the cork at a height that is different from the first drop. Does the wavelength depend upon how high above the water the cork is dropped?
Example 1: Calculate the Velocity of Wave Propagation: Gull in the Ocean
Calculate the wave velocity of the ocean wave in Figure 2 if the distance between wave crests is 10.0 m and the time for a sea gull to bob up and down is 5.00 s.
Strategy
We are asked to find [latex]{v_{\text{w}}}.[/latex] The given information tells us that [latex]{\lambda=10.0\text{ m}}[/latex] and [latex]{T=5.00\text{ s}}.[/latex] Therefore, we can use [latex]{v_{\text{w}}=\frac{\lambda}{T}}[/latex] to find the wave velocity.
Solution
- Enter the known values into [latex]{v_{\text{w}}=\frac{\lambda}{T}}:[/latex]
[latex]{v_{\text{w}}\:=}[/latex] [latex]{\frac{10.0\text{ m}}{5.00\text{ s}}}.[/latex]
- Solve for [latex]{v_{\text{w}}}[/latex] to find [latex]{v_{\text{w}}= 2.00\text{ m/s}}.[/latex]
Discussion
This slow speed seems reasonable for an ocean wave. Note that the wave moves to the right in the figure at this speed, not the varying speed at which the sea gull moves up and down.
Transverse and Longitudinal Waves
A simple wave consists of a periodic disturbance that propagates from one place to another. The wave in Figure 3 propagates in the horizontal direction while the surface is disturbed in the vertical direction. Such a wave is called a transverse wave or shear wave; in such a wave, the disturbance is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation. Figure 4 shows an example of a longitudinal wave. The size of the disturbance is its amplitude X and is completely independent of the speed of propagation [latex]{v_{\text{w}}}.[/latex]
Waves may be transverse, longitudinal, or a combination of the two. (Water waves are actually a combination of transverse and longitudinal. The simplified water wave illustrated in Figure 2 shows no longitudinal motion of the bird.) The waves on the strings of musical instruments are transverse—so are electromagnetic waves, such as visible light.
Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and thus the sound waves in them must be longitudinal or compressional. Sound in solids can be both longitudinal and transverse.
Earthquake waves under Earth’s surface also have both longitudinal and transverse components (called compressional or P-waves and shear or S-waves, respectively). These components have important individual characteristics—they propagate at different speeds, for example. Earthquakes also have surface waves that are similar to surface waves on water.
Check Your Understanding
1: Why is it important to differentiate between longitudinal and transverse waves?
 Wiggle the end of the string and make waves, or adjust the frequency and amplitude of an oscillator. Adjust the damping and tension. The end can be fixed, loose, or open.
Section Summary
- A wave is a disturbance that moves from the point of creation with a wave velocity [latex]{v_{\text{w}}}.[/latex]
- A wave has a wavelength [latex]{\lambda},[/latex] which is the distance between adjacent identical parts of the wave.
- Wave velocity and wavelength are related to the wave’s frequency and period by [latex]{v_{\text{w}}=\frac{\lambda}{T}}[/latex] or [latex]{v_{\text{w}}=f\lambda}.[/latex]
- A transverse wave has a disturbance perpendicular to its direction of propagation, whereas a longitudinal wave has a disturbance parallel to its direction of propagation.
Conceptual Questions
1: Give one example of a transverse wave and another of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each.
2: What is the difference between propagation speed and the frequency of a wave? Does one or both affect wavelength? If so, how?
Problems & Exercises
1: Storms in the South Pacific can create waves that travel all the way to the California coast, which are 12,000 km away. How long does it take them if they travel at 15.0 m/s?
2: Waves on a swimming pool propagate at 0.750 m/s. You splash the water at one end of the pool and observe the wave go to the opposite end, reflect, and return in 30.0 s. How far away is the other end of the pool?
3: Wind gusts create ripples on the ocean that have a wavelength of 5.00 cm and propagate at 2.00 m/s. What is their frequency?
4: How many times a minute does a boat bob up and down on ocean waves that have a wavelength of 40.0 m and a propagation speed of 5.00 m/s?
5: Scouts at a camp shake the rope bridge they have just crossed and observe the wave crests to be 8.00 m apart. If they shake it the bridge twice per second, what is the propagation speed of the waves?
6: What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at 0.800 m/s?
7: What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to another city 84.0 km away in 12.0 s?
8: Radio waves transmitted through space at [latex]{3.00\times10^8\text{ m/s}}[/latex] by the Voyager spacecraft have a wavelength of 0.120 m. What is their frequency?
9: Your ear is capable of differentiating sounds that arrive at the ear just 1.00 ms apart. What is the minimum distance between two speakers that produce sounds that arrive at noticeably different times on a day when the speed of sound is 340 m/s?
10: (a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, they compare the arrival times of S- and P-waves, which travel at different speeds. Figure 7) If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)
Glossary
- longitudinal wave
- a wave in which the disturbance is parallel to the direction of propagation
- transverse wave
- a wave in which the disturbance is perpendicular to the direction of propagation
- wave velocity
- the speed at which the disturbance moves. Also called the propagation velocity or propagation speed
- wavelength
- the distance between adjacent identical parts of a wave
Solutions
Check Your Understanding
In the different types of waves, energy can propagate in a different direction relative to the motion of the wave. This is important to understand how different types of waves affect the materials around them.
Problems & Exercises
1:
[latex]{t=9.26\text{ d}}[/latex]
3:
[latex]{f=40.0\text{ Hz}}[/latex]
5:
[latex]{v_{\text{w}}=16.0\text{ m/s}}[/latex]
7:
[latex]{\lambda\:=\:700\text{ m}}[/latex]
9:
[latex]{d=34.0\text{ cm}}[/latex]