The fundamental frequency of a closed pipe is | vedclass

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(B) Let the length of the closed pipe be $L_{1}$ and the length of the open pipe be $L_{2}$.The fundamental frequency of a closed pipe is given by $v_

Vedclass · Accepted Answer

$1: 4$

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(B) Let the length of the closed pipe be $L_{1}$ and the length of the open pipe be $L_{2}$.The fundamental frequency of a closed pipe is given by $v_{1} = \frac{v}{4 L_{1}}$.The frequency of the second harmonic of an open pipe is given by $v_{2} = 2 	imes \frac{v}{2 L_{2}} = \frac{v}{L_{2}}$.According to the problem,the fundamental frequency of the closed pipe is equal to the frequency of the second harmonic of the open pipe,so $v_{1} = v_{2}$.Substituting the expressions,we get $\frac{v}{4 L_{1}} = \frac{v}{L_{2}}$.Rearranging the terms,we find $\frac{L_{1}}{L_{2}} = \frac{1}{4}$.Thus,the ratio of their lengths is $1: 4$.

The fundamental frequency of a closed pipe is equal to the frequency of the second harmonic of an open pipe. The ratio of their lengths is

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