The fundamental frequency of an open organ pipe corresponds to the D above middl

Question

The fundamental frequency of an open organ pipe corresponds to the D above middle C (293.7 Hz on the chromatic musical scale). The third resonance of a closed organ pipe has the same frequency. (Assume that the speed of sound in air is 343 m/s.) What is the length of the open pipe? Your response differs from the correct answer by more than 10%. Double check your calculations. What is the length of the closed pipe? Your response differs from the correct answer by more than 10%. Double check your calculations.

Explanation / Answer

the equation for both ends being open is given by the following...

f=nV/2L

the equation for one end being closed is given by the following...

f=nV/4L


_________________________________
f=frequency
n=harmonic number
V=velocity of the wave, in this case it's sound so u use the average speed of sound (343m/s)
L=length of pipe
--------------------------------------...


k now just plug in and solve for both "L"s



for the first pipe...

293.7=(1)(343)/{(2)L}

solve for L and you get L=0.583

for the second one.....

293.7=(3)(343)/{(4)L}

solve for L and you get L=0.875


so then you do 0.875/0.583= about 1.5m

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