On closing an open organ pipe from one end,it | vedclass

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(B) Let the length of the pipe be $\ell$ and the velocity of sound be $V$.For an open organ pipe,the fundamental frequency is $f_{open} = \frac{V}{2\e

Vedclass · Accepted Answer

$100$

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(B) Let the length of the pipe be $\ell$ and the velocity of sound be $V$.For an open organ pipe,the fundamental frequency is $f_{open} = \frac{V}{2\ell}$.When one end is closed,the pipe becomes a closed organ pipe. The harmonics of a closed organ pipe are odd multiples of the fundamental frequency $f_{closed} = \frac{V}{4\ell}$.The third harmonic of a closed organ pipe is $f_{3, closed} = 3 	imes \frac{V}{4\ell} = \frac{3V}{4\ell}$.According to the problem,$f_{3, closed} - f_{open} = 50 ~Hz$.Substituting the expressions: $\frac{3V}{4\ell} - \frac{V}{2\ell} = 50$.$\frac{3V - 2V}{4\ell} = 50 \implies \frac{V}{4\ell} = 50 ~Hz$.We need to find the fundamental frequency of the open pipe,$f_{open} = \frac{V}{2\ell} = 2 	imes \frac{V}{4\ell} = 2 	imes 50 = 100 ~Hz$.

On closing an open organ pipe from one end,it is noticed that the frequency of the third harmonic is $50 ~Hz$ more than the fundamental frequency of vibration in the open organ pipe. The fundamental frequency of the open organ pipe is (in $~Hz$)

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