The difference between the fundamental freque | vedclass

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(A) Let $v$ be the speed of sound and $l$ be the length of the pipes.For an open organ pipe,the fundamental frequency is $f_{o} = \frac{v}{2l}$.For a

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$100$

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(A) Let $v$ be the speed of sound and $l$ be the length of the pipes.For an open organ pipe,the fundamental frequency is $f_{o} = \frac{v}{2l}$.For a closed organ pipe,the fundamental frequency is $f_{c} = \frac{v}{4l}$.Given that the difference between these fundamental frequencies is $100 \ Hz$:$f_{o} - f_{c} = 100 \ Hz \implies \frac{v}{2l} - \frac{v}{4l} = 100 \ Hz \implies \frac{v}{4l} = 100 \ Hz$.The second harmonic of the open pipe is $f_{2,o} = 2 	imes f_{o} = 2 	imes \frac{v}{2l} = \frac{v}{l}$.The third harmonic of the closed pipe is $f_{3,c} = 3 	imes f_{c} = 3 	imes \frac{v}{4l} = \frac{3v}{4l}$.The difference between these frequencies is:$f_{2,o} - f_{3,c} = \frac{v}{l} - \frac{3v}{4l} = \frac{4v - 3v}{4l} = \frac{v}{4l}$.Since $\frac{v}{4l} = 100 \ Hz$,the required difference is $100 \ Hz$.

The difference between the fundamental frequencies of an open pipe and a closed pipe of the same length is $100 \ Hz$. The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is: (in $Hz$)

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