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  4. A longitudinal sound wave given by P=25sin(π /2)(x - 660 t) ( P is in Nm- 2 and x is in m and t is in s ) is sent down a closed organ pipe. If the pipe vibrates in second overtone then the length of the pipe (in m ) is :

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Q. A longitudinal sound wave given by $P=25sin\frac{\pi }{2}\left(x - 660 t\right)$ ( $P$ is in $Nm^{- 2}$ and $x$ is in $m$ and $t$ is in $s$ ) is sent down a closed organ pipe. If the pipe vibrates in second overtone then the length of the pipe (in $m$ ) is :

NTA AbhyasNTA Abhyas 2022

Solution:

$K=\frac{\pi }{2}=\frac{2 \pi }{\lambda }\Rightarrow \lambda =4$
Second overtone $\Rightarrow \frac{5 \lambda }{4}=L\Rightarrow L=5m$