Musical instruments and resonance

I’ve started a project exploring musical instruments and the physics controlling their audio properties. Mostly I’m interested in brass instruments like a trumpet or trombone‒instruments that are tubular for much of their length. Brass instruments have a constant diameter at their beginning. As the tube approaches the end, the instruments become more conical until terminating in a flared bell. I chose them because I played the trumpet in high school. It’s familiar.

One book that I’m using to help understand what is happening is “The Physics of Musical Instruments, 2nd edition” by Neville H. Fletcher and Thomas D. Rossing. It has quantitative descriptions of the properties of real instruments.

One interesting idea is to consider brass instruments as “reed instruments.” For a brass instrument, the “reed” is the lips of the performer. This allows brass instruments to use the same equations as woodwinds. As a first approximation, lips and reeds have similar properties of interrupted air flow. It does make a difference whether the opening closes with increasing pressure or opens with increasing pressure so the analogy has its limits.

My first experiments have been with a pipe resonating at different frequencies. My method of creating data is to input a sweeping pitched sound to one end of a pipe with a speaker. The pipe resonates at different frequencies so that the intensity of the sound so the other end varies over time. This is a example configuration with headphones presenting the sound on the right end and a microphone picking up sound on the left. I haven’t calibrated the frequency response curve of the microphone and speakers.

For example, when I sweep the input sine wave from 50 Hz to 2000 Hz over 2 minutes on one end of a 1m 1/2″ PVC tube, the amplitude from the other end creates this graph. I measure the amplitude as rms (root mean square) by squaring the values of each sample in a block and then taking their average. This helps in comparing one block to the next.

time vs. amplitude

One thing I notice with such examples is that as the frequency goes up, there is more and more noise in the wave form. The shapes become more ragged. It should be easy to identify the time of the different peaks and thus their frequency but this and other sources of noise interfere.

If I take above run and make an image of its frequency distribution, I get this. The Y axis isn’t calibrated, but starts at 0Hz at the bottom. This chart has the whole duration of a single observation session. The graph above is trimmed to exclude the times that I wasn’t activating the system.

Time vs. frequency

An interesting feature of the graph are the higher overtones from the input sweep. They show up as lines with higher slopes than the main output. This example, I can see 4 extra lines, but different configurations of microphone and pipe may show only one or two. (The third overtone is barely visible above the middle of the run.) Also, if I look closely, I see very faint equispaced horizontal lines. I suspect that those are from my computer fan but I haven’t verified it.

The gray noise at the bottom of the graph are different noises from within my house. I haven’t identified the causes of those or their frequency. Some of the graph is marked with mechanical bumps that show up as lines starting at zero hertz. The vertical features centered on the main input frequency are a common feature of these charts. I’m not sure whether they are real or are an artifact of my processing.

(This representation doesn’t help me identify the position of the peaks.)

An interesting adjustment is needed when I break the signal into chunks. For the Fourier transform or other analyses, I need to block the chunks so that they end at the zero crossings of the input waveform. I pick a minimum number of samples for a block and then search further for the next positively sloped zero crossing. If I don’t do that, the sharp edges at the ends of a block add artifacts that hide real effects. The software I’m using for FFT, FFTW allows me to have non-power-of-two long blocks which is essential for seeing useful results.

Review: Blinded by the Light (2019)

A reel of movie film
In Blinded by the Light, the first advice of dad for his son’s entry to a new school is “Stay away from the girls.” Javed, played by Viveik Karla, is a teenager in Luton, Great Britain whose parents emigrated from Pakistan. He longs to escape the nowhere town and hopes college will lead to a career as a writer. He has been an avid writer with years of journals lined up in his room. School can become his road to escape.

Javed’s longtime friend, Matt, played by Dean-Charles Chapman, is a musician whom Javed helps by writing lyrics. Matt’s frustrated with the political stock of Javed’s songs: they’re not performable. He still holds out hope for Javed’s lyrics getting better.

Javed’s father, played by Kulvinder Ghir, is an immigrant from Pakistan. He is the center of the household and manages the household’s money. The traditional role of the father is a struggle for Javed’s father when circumstances change. Unlike in Fiddler on the Roof, the family is not torn apart by events beyond their control. However, events beyond their control such as the recession under Margaret Thatcher still make them stretch and evolve.

Javed meets Roops at school. Roops, played by Aaron Phagura, gives Javed some Bruce Springsteen cassettes. The songs revolutionize Javed’s attitude and fill him with power. He feels that the music speaks directly to him. Springsteen puts words to his feelings and cinematically, the words are visually swirling around Javed as he listens.

Central to the progression of Javed as a writer is his teacher Ms. Clay, played by Hayley Atwell. She scolds him for not sharing with the world the raw emotion in his writing when he discards his poems. He follows her inspiration and writes in the school paper and then a local newspaper. Javed’s cultural background and knowledge of Urdu allow him to write a powerful story about the community’s mosque.

While the movie isn’t exactly a musical, music has a central place to the story. The movie is full of the angst and joy of youth. Javed and Roops go to New Jersey after he wins a writing contest. During the trip, the friends make a pilgrimage to visit Bruce Springsteen’s hometown sites.

One of the struggles that Javed’s family faces is the hostility of some people in their community toward Pakistani immigrants. Javed’s family faces those indignities with grace and do not become bitter when life becomes more difficult.

Blinded by the Light is an melange of conflicting cultures. The Pakistani community, the people hostile to them, students at the high school, and Javed’s friends all mix together into a scene of hope that is inspired by Bruce.

Need any Passengers?





Spring 2018 random notes

I ordered the book Homecoming by John Bradshaw tonight. I checked for prices, but pretty much ignored that website. It listed two used bookstore services I have accounts with, and Alibris lost the sale because their checkout screen failed. Amazon, I avoid on principle.

I conjured up some one-time-use credit card numbers. They’re great for online purchases because they put a (lower) limit on the risk from bad people stealing my information from a vendor’s databases. It comes from Bank of America’s “ShopSafe” which is a service on their online banking site.

I got a long, relaxing nap this afternoon/evening. I woke up at 7:05 which was a little late for some events I wanted to go to that started at 7. I could have gone late, but I chose not to.

I really like my new sofa. The old one was tore up by my cats. I’d had it for years. I have been having trouble with back pain sitting on the old one so I needed to take action. Thanks mom!

I’ve got to the Y three days in a row which is a big accomplishment for me.

I made an appointment for Friday with the nurse with my cardiologist. I am concerned how badly winded I got moving the furniture with my dad. It shows that blood pressure might be an wishful explanation of my cardiac condition. I was upset the cardiologist had let my blood pressure be dangerously high for months while he said it was ok. I canceled my last appointment in March when I finally forced the issue. At that time, he told me my goal level was quite below those levels. Right now it is quite consistently a good number. It’s in the universally recommended range so I’m happier…. Also that I’m only taking one medication instead of the 2+ that I’d been taking until March.

There’s an famous-ish song Dragostea din tei that had a viral video that made it famous. Back when I first learned about the song, I found a musician Craig Anstey on youtube that had done a cover of it. I have a copy of his cover that I have for making a mix tape (BQM XVII). It’s not a literal translation of the lyrics, but its text is well known.

My last cousin is engaged. The wedding is Sept. 15. We’ll all be packing up and going to Louisiana for the festivities. Of the 15 in our generation I’ll be the only one not married and it is most likely going to stay that way. There’s also been only 2 divorces among us which is a point of pride for me — of the 6 pairs of married aunts and uncles, they have a combined 300+ years married.

On the most recent royal wedding in Great Britain I liked that the officiator of the wedding said “I proclaim them man and wife.” I don’t think “proclaim” is used much (at least it sounds more elevated than the language I remember from my family’s weddings.)

I was able to run the media for my church this week. I had someone behind me helping my confidence. There were a couple of places where he suggested I black the screen that I didn’t notice on my own. The social media feed was a little messy to turn off, but I remembered the right way to do that so it was not broken for long.

I guess I’ve typed enough….




Dome with clematis











Recently, Pandora put on one of my feeds “Year of the Cat” by Al Stewart.

I hadn’t heard the song for a long time and after hearing it a few times, I decided I wanted more like it.

I created a Year of the Cat channel and have been rewarded with a lot of nostalgia.

With my tablet playing it, I get all of the late 70s music I could ever ask for.

Some of it is pretty awful, but I get a lot of nice memories from the non-awful stuff.