The frequency of the third overtone of a pipe | vedclass

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(B) For a pipe closed at one end,the frequency of the $n^{th}$ overtone is given by $f = \frac{(2n+1)V}{4L_c}$.For the third overtone,$n=3$,so $f = \f

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$1: 2$

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(B) For a pipe closed at one end,the frequency of the $n^{th}$ overtone is given by $f = \frac{(2n+1)V}{4L_c}$.For the third overtone,$n=3$,so $f = \frac{(2 	imes 3 + 1)V}{4L_c} = \frac{7V}{4L_c}$.For a pipe open at both ends,the frequency of the $n^{th}$ overtone is given by $f = \frac{(n+1)V}{2L_o}$.For the sixth overtone,$n=6$,so $f = \frac{(6+1)V}{2L_o} = \frac{7V}{2L_o}$.Equating the two frequencies: $\frac{7V}{4L_c} = \frac{7V}{2L_o}$.Simplifying,we get $\frac{1}{4L_c} = \frac{1}{2L_o}$,which implies $\frac{L_c}{L_o} = \frac{2}{4} = \frac{1}{2}$.

The frequency of the third overtone of a pipe of length $L_c$,closed at one end,is the same as the frequency of the sixth overtone of a pipe of length $L_o$,open at both ends. Then the ratio $L_c : L_o$ is

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