Resonance/Harmonic frequencies in open/closed pipes

Doc Z

1. The problem statement, all variables and given/known data
The fundamental frequency of an open organ pipe corresponds to E above middle C (329.6 Hz on the chromatic musical scale). The third resonance of a different closed organ pipe has the same frequency. What are the lengths of the two pipes?


2. Relevant equations
natural frequency of an air column open at both ends - f=nv/2L

and

natural frequency of an air column closed at one end - f=nv/4L

3. The attempt at a solution

I figured out the length of the open pipe by using the first equation. My answer is .520m.

Now, for the closed pipe, since the third resonance frequency of the closed pipe is the same, I used the second equation in the following way - f=3v/4L. However, this is wrong because I should not be using the third harmonic. The question references the 3rd resonance, not the third harmonic, but I have no idea where to go from here. I don't even know what equation to use. Any suggestions?

Thanks for the help!

Doc Z

Wow I sure feel smart...the third resonance=fifth harmonic! lol sorry guys.