How Long Should an Organ Pipe Be to Resonate at 16.4 Hz?

[viciousp]

Homework Statement

The Lowest note on an organ is 16.4 Hz.
a. What is the shortest pen organ that will resonate at this frequency
b. What is the pitch of the same organ pipe is closed

Homework Equations

f=V(n)/2L, n=1,2,3..
f=V(n)/4L, n-1,3,5...

The Attempt at a Solution

I understand how to do this problem , such as setting up the equation as 16.4=V(1)/2L and solve for V then you should get 16.4Hz= 32.8L/2L, but with that any L short of zero can work. I am thinking that there is not enough information to solve this problem anyone else have an idea?

 

[heth]

If you had to explain to someone who'd not done this part of a physics course what each of the letters in your equations (f, V, n and L) mean, what would you say?My recommendation would be to drop these equations. Draw the organ pipe and the wave / part-wave, then continue the sketch so that a whole wavelength is included.

That way, you can actually see how the wave and pipe relate to each other. This breaks the problem down into simpler problems that you can already do. And, most importantly, it helps you to understand the physics rather than plucking some equations from a book and throwing numbers at them. So you'll be able to use your understanding to do other problems in the future.

 

[thomate1]

You are correct that there is not enough information to solve this problem. In order to determine the length of the pipe, we would also need to know the speed of sound in the medium (in this case, air). Additionally, the type of pipe (open or closed) would also affect the equation used to solve for the length. It is important to have all necessary information in order to accurately solve a problem.