A pipe open at both ends has a fundamental fr | vedclass

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(B) For an open pipe of length $\ell$,the fundamental frequency is given by $f = \frac{V}{2\ell}$,where $V$ is the speed of sound in air.When the pipe

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(B) For an open pipe of length $\ell$,the fundamental frequency is given by $f = \frac{V}{2\ell}$,where $V$ is the speed of sound in air.When the pipe is dipped vertically in water to half of its length,the effective length of the air column becomes $\ell' = \frac{\ell}{2}$.Since one end is now closed by the water surface,the pipe acts as a closed organ pipe (one end open,one end closed).The fundamental frequency of a closed pipe of length $\ell'$ is given by $f' = \frac{V}{4\ell'}$.Substituting $\ell' = \frac{\ell}{2}$ into the formula,we get $f' = \frac{V}{4(\ell/2)} = \frac{V}{2\ell}$.Comparing this with the initial frequency,we find $f' = f$.

$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to

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