The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the

Question

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is

Accepted Answer

For a closed organ pipe, the third harmonic frequency is $f_c = \frac{3v}{4l}$. For an open organ pipe, the fundamental frequency is $f_o = \frac{v}{2l'}$. Given $f_o = f_c$, so $\frac{v}{2l'} = \frac{3v}{4l}$. Thus, $l' = \frac{4l}{3 	imes 2} = \frac{2l}{3} = \frac{2 	imes 20}{3} = 13.33 	ext{ cm}$. Note: The provided answer key in the image says (3) 13.2 cm, but the calculation yields 13.33 cm.

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