The 3^{text{rd}} overtone of a closed organ p | vedclass

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(A) For a closed organ pipe of length $L_c$,the frequency of the $n^{	ext{th}}$ overtone is given by $f_c = \frac{(2n+1)v}{4L_c}$,where $n$ is the ov

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$\frac{7}{8}$

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(A) For a closed organ pipe of length $L_c$,the frequency of the $n^{	ext{th}}$ overtone is given by $f_c = \frac{(2n+1)v}{4L_c}$,where $n$ is the overtone number.For the $3^{	ext{rd}}$ overtone $(n=3)$,$f_c = \frac{(2(3)+1)v}{4L_c} = \frac{7v}{4L_c}$.For an open organ pipe of length $L_o$,the frequency of the $n^{	ext{th}}$ overtone is given by $f_o = \frac{(n+1)v}{2L_o}$.For the $3^{	ext{rd}}$ overtone $(n=3)$,$f_o = \frac{(3+1)v}{2L_o} = \frac{4v}{2L_o} = \frac{2v}{L_o}$.Since the frequencies are in unison,$f_c = f_o$:$\frac{7v}{4L_c} = \frac{2v}{L_o}$.Rearranging for the ratio $\frac{L_c}{L_o}$:$\frac{L_c}{L_o} = \frac{7}{4 	imes 2} = \frac{7}{8}$.Thus,the correct option is $A$.

The $3^{\text{rd}}$ overtone of a closed organ pipe is in unison with the $3^{\text{rd}}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

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