Resonance/Harmonic frequencies in open/closed pipes

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SUMMARY

The discussion centers on calculating the lengths of an open organ pipe and a closed organ pipe, both resonating at the same fundamental frequency of 329.6 Hz. The fundamental frequency for the open pipe is determined using the formula f = nv/2L, resulting in a length of 0.520 meters. For the closed pipe, the user initially misapplies the harmonic concept but later clarifies that the third resonance corresponds to the fifth harmonic, necessitating a different approach for accurate length calculation.

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Homework Statement


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?

Homework 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

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

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