Question

In pipe A, the ratio of a particular harmonic frequency to the next lower harmonic frequency is 1.2. In pipe B, the ratio of a particular harmonic frequency to the next lower harmonic frequency is 1.4. How many open ends are in pipe A and pipe B?

I'm not sure exactly how to go about solving this. I know the equations for harmonies frequencies for pipes with two open ends and with one open ends, but I must be missing something fundamental here because I'm not sure what to do.

Answer 1

Hint:

1.2 = 6/5

1.4 = 7/5

Answer 2

I think I figured it out. For the first one, I set up the equation like so: \[\frac{ n }{n-1}=1.2\] Once I had that, I solved for n, which, as you said, ended up being 6. So the ratio was 6/5. Because there was a single integer between the top and bottom, that meant that the pipe had two open ends.

I used a similar argument for part (b), but I just set the bottom of the ration equal to n-2 and got the correct answer.

Thanks for your help!