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(B) The fundamental frequency of an open tube of length $L$ is given by $f_0 = \frac{v}{2L}$,where $v$ is the speed of sound in air.When the tube is d

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$f_0$

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(B) The fundamental frequency of an open tube of length $L$ is given by $f_0 = \frac{v}{2L}$,where $v$ is the speed of sound in air.When the tube is dipped vertically into water such that half of its length is inside the water,the tube effectively becomes a closed pipe (closed at one end by the water surface) with a new length $L' = L/2$.The fundamental frequency of a closed pipe of length $L'$ is given by $f' = \frac{v}{4L'}$.Substituting $L' = L/2$ into the formula,we get $f' = \frac{v}{4(L/2)} = \frac{v}{2L}$.Comparing this with the original frequency,we find $f' = f_0$.

$A$ cylindrical tube,open at both ends,has a fundamental frequency $f_0$ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is

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