The frequency of the fifth harmonic of a clos | vedclass

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(A) For an open organ pipe,the frequency of the $n^{th}$ harmonic is given by $f_n = \frac{n v}{2 l_o}$.For the third harmonic $(n=3)$,$f_{open} = \fr

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$60$

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(A) For an open organ pipe,the frequency of the $n^{th}$ harmonic is given by $f_n = \frac{n v}{2 l_o}$.For the third harmonic $(n=3)$,$f_{open} = \frac{3 v}{2 l_o}$.Given $l_o = 72 \ cm$,so $f_{open} = \frac{3 v}{2 	imes 72} = \frac{v}{48}$.For a closed organ pipe,the frequency of the $n^{th}$ harmonic (where $n$ is odd) is given by $f_n = \frac{n v}{4 l_c}$.For the fifth harmonic $(n=5)$,$f_{closed} = \frac{5 v}{4 l_c}$.According to the problem,$f_{closed} = f_{open}$.$\frac{5 v}{4 l_c} = \frac{3 v}{2 l_o}$.Substituting $l_o = 72 \ cm$:$\frac{5}{4 l_c} = \frac{3}{2 	imes 72} = \frac{3}{144} = \frac{1}{48}$.$4 l_c = 5 	imes 48 = 240$.$l_c = \frac{240}{4} = 60 \ cm$.

The frequency of the fifth harmonic of a closed pipe is equal to the frequency of the third harmonic of an open pipe. If the length of the open pipe is $72 \ cm$,then the length of the closed pipe is: (in $cm$)

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