Question

E fundamental frequency of an open organ pipe corresponds to the middle c (261.6 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.) (a) what is the length of the open pipe

Answer 1

The wavelength of the third resonance of the closed organ pipe is equal to the ratio between the speed of sound and the frequency of the 3rd harmonic:

$\lambda_3 = \frac{c}{f_3}=\frac{343 m/s}{261.6 Hz} =1.31 m$

The relationship between length of a closed pipe and wavelength of the standing waves inside is:

$L=\frac{n}{4}\lambda_n$

where n is the number of the harmonic. In this case, n=3, so the length of the pipe is

$L=\frac{3}{4}(1.31 m)=0.98 m$