The lengths of the two pipes open at both end | vedclass

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(C) For a pipe open at both ends, the fundamental frequency is given by $f = \frac{v}{2l}$, where $v$ is the velocity of sound and $l$ is the length o

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$\frac{vL_1}{2L(L + L_1)}$

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(C) For a pipe open at both ends, the fundamental frequency is given by $f = \frac{v}{2l}$, where $v$ is the velocity of sound and $l$ is the length of the pipe.For the first pipe of length $L$, the frequency is $f_1 = \frac{v}{2L}$.For the second pipe of length $(L + L_1)$, the frequency is $f_2 = \frac{v}{2(L + L_1)}$.The beat frequency is the difference between the two frequencies: $f_b = |f_1 - f_2|$.$f_b = \left| \frac{v}{2L} - \frac{v}{2(L + L_1)} \right| = \frac{v}{2} \left| \frac{(L + L_1) - L}{L(L + L_1)} \right|$.$f_b = \frac{v}{2} \left( \frac{L_1}{L(L + L_1)} \right) = \frac{vL_1}{2L(L + L_1)}$.

The lengths of the two pipes open at both ends are $L$ and $(L + L_1)$. If they are sounded together, the beat frequency will be ($v$ = velocity of sound in air)

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