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(C) For an open organ pipe of length $L$,the frequency of the $P^{	ext{th}}$ overtone is given by $f_{	ext{open}} = (P+1) \frac{v}{2L}$.For a closed

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$\frac{2(P+1)}{2P+1}$

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(C) For an open organ pipe of length $L$,the frequency of the $P^{	ext{th}}$ overtone is given by $f_{	ext{open}} = (P+1) \frac{v}{2L}$.For a closed organ pipe of the same length $L$,the frequency of the $P^{	ext{th}}$ overtone is given by $f_{	ext{closed}} = (2P+1) \frac{v}{4L}$.Taking the ratio of the frequency of the $P^{	ext{th}}$ overtone of the open pipe to that of the closed pipe:Ratio $= \frac{(P+1) \frac{v}{2L}}{(2P+1) \frac{v}{4L}}$.Ratio $= \frac{P+1}{2L} 	imes \frac{4L}{2P+1} = \frac{2(P+1)}{2P+1}$.

$A$ pipe open at both ends and a pipe closed at one end have the same length. The ratio of the frequencies of their $P^{\text{th}}$ overtone is:

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