An organ pipe P_1 closed at one end is vibrat | vedclass

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(B) For a pipe $P_1$ closed at one end,the frequency of the $n$-th overtone is given by $f_n = (2n+1) \frac{v}{4L_1}$. For the first overtone $(n=1)$,

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$3/8$

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(B) For a pipe $P_1$ closed at one end,the frequency of the $n$-th overtone is given by $f_n = (2n+1) \frac{v}{4L_1}$. For the first overtone $(n=1)$,$f_1 = 3 \frac{v}{4L_1}$.For a pipe $P_2$ open at both ends,the frequency of the $n$-th overtone is given by $f_n = (n+1) \frac{v}{2L_2}$. For the third overtone $(n=3)$,$f_3 = (3+1) \frac{v}{2L_2} = 4 \frac{v}{2L_2} = 2 \frac{v}{L_2}$.Since both pipes are in resonance with the same tuning fork,their frequencies are equal: $3 \frac{v}{4L_1} = 2 \frac{v}{L_2}$.Rearranging the terms to find the ratio $L_1/L_2$: $\frac{L_1}{L_2} = \frac{3}{4 	imes 2} = \frac{3}{8}$.

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

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