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Superposition of Waves — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsSuperposition of Waves4 Marks
Question
A pipe open at both ends has the fundamental frequency $n$. If the pipe is immersed vertically in water up to half its length, what would be the fundamental frequency of the resulting air column?
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Answer


Let $L$ be the length of the pipe open at both ends whose fundamental frequency is $n$. Then, ignoring the end correction, $n =\frac{v}{2 L}$
where $v$ is the speed of sound in air.
When the pipe is immersed vertically in water up to half its length, it becomes a pipe closed at one end with an air column of length $L^{\prime}=L / 2$. Then, its fundamental frequency $n^{\prime}$ is
$
n^{\prime}=\frac{v}{4 L^{\prime}}=\frac{v}{4(L / 2)}=\frac{v}{2 L}
$
which is equal to $n$, the fundamental frequency of the open pipe.

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