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

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(A) The frequency of the $m^{	ext{th}}$ harmonic in an open organ pipe is given by $f_m = \frac{m v}{2 L}$.For the fundamental frequency $(m=1)$, $f_

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$100$

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(A) The frequency of the $m^{	ext{th}}$ harmonic in an open organ pipe is given by $f_m = \frac{m v}{2 L}$.For the fundamental frequency $(m=1)$, $f_1 = \frac{v}{2 L}$.The frequency of the $n^{	ext{th}}$ harmonic in a closed organ pipe is given by $f_n^{\prime} = \frac{n v}{4 L}$, where $n$ must be an odd integer.The frequency of the $3^{	ext{rd}}$ harmonic in a closed organ pipe is $f_3^{\prime} = \frac{3 v}{4 L}$.According to the problem, $f_3^{\prime} - f_1 = 50 \,Hz$.Substituting the expressions: $\frac{3 v}{4 L} - \frac{v}{2 L} = 50$.$\frac{3 v - 2 v}{4 L} = 50 \Rightarrow \frac{v}{4 L} = 50 \Rightarrow \frac{v}{L} = 200$.The fundamental frequency of the open organ pipe is $f_1 = \frac{v}{2 L} = \frac{200}{2} = 100 \,Hz$.

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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