Question

Equation of longitudinal stationary wave in second overtone mode in a closed organ pipe is $y=\left(4mm\right)sin\pi xcos\pi t$ Here x is in metre and t in second. Then match the following two columns:

Answer 1

equation of wave $S=Asin(kx-\omega t)$

$kx=\pi x$

$l=\frac{2\pi }{\lambda }=\pi$

$\lambda =2$

in second overtone

$L=\frac{4\lambda }{5}=1.6m$

from closed end one displacement node is at $\frac{2\lambda }{4}=1m$ and other at $\frac{4\lambda }{4}=2m$

distance of pressure node is at $\frac{3\lambda }{4}=1.5m$