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Echo Ranging Formula


Last week I used a stopwatch to measure the echo time of my snare drum in the hall outside my classroom, which is 80 meters long. The average echo time was 10 milliseconds. Use your understanding of the Echo Ranging formula to prove or disprove my findings, remember this echo was heard in air.


Solution Preview

Formula used is d=ct
where d=distance, c=speed, t=time

In the given problem, d=80*2=160 (because, 80m is one ...

Solution Summary

The solution is well explained. The solution can be easily understood by anyone with moderate understanding of the topic. Overall, a great response to the question being asked.

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Using the Master Theorem

This problem stems from the Master Theorem. I have a sample problem with a solution but it does not show me the steps to reduce the problem algebraically and I don't see how they got to the solution.

The problem is:

T(n) = 6T(n/5) + n^2 -8n + 3

Using the Master Theorem this problem falls under case 3 in which we have to solve for regularity. Which is of the form

af(n/b) <= cf(n), where a = 6, b = 5 and f(n) = n^2 -8n + 3

So we have the formula:

6((n/5)^2 - (8n/5) + 3) <= c(n^2 - 8n + 3)

Then in the solution I have, it states that after carrying out the algebra we get:

((6/25 - c)n^2 + 15) <= 8n.

I can not see how they came to this conclusion. Is this a correct solution to this inequality and if so, could you show me the steps as to how they arrived at this solution?

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