A pipe open at both ends produces a fundament | vedclass

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(A) Let the length of the pipe be $L$. For an open pipe,the fundamental frequency is $n_1 = \frac{v}{2L}$,where $v$ is the speed of sound in air.When

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$1/2$

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(A) Let the length of the pipe be $L$. For an open pipe,the fundamental frequency is $n_1 = \frac{v}{2L}$,where $v$ is the speed of sound in air.When $\frac{3}{4}$ of the pipe is submerged in water,the length of the air column remaining above the water is $L' = L - \frac{3}{4}L = \frac{1}{4}L$.This pipe now acts as a closed pipe (closed at one end by water). The fundamental frequency of a closed pipe of length $L'$ is $n_2 = \frac{v}{4L'}$.Substituting $L' = \frac{1}{4}L$ into the expression for $n_2$,we get $n_2 = \frac{v}{4(\frac{1}{4}L)} = \frac{v}{L}$.Now,calculating the ratio $\frac{n_1}{n_2} = \frac{v/2L}{v/L} = \frac{v}{2L} 	imes \frac{L}{v} = \frac{1}{2}$.

$A$ pipe open at both ends produces a fundamental frequency $n_1$. When the pipe is kept with $\frac{3}{4}$ of its length in water,it produces a note of fundamental frequency $n_2$. The ratio of $\frac{n_1}{n_2}$ is

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