A standing wave in a pipe with a length $L=1.2 \,m$ is described by $y(x, t)=y_0 \sin [(2 \pi / L) x] \sin [(2 \pi / L) x+\pi / 4]$ based on above information, which one of the following statement is incorrect? (Speed of sound in air is $300 \,ms ^{-1}$ )
KVPY 2012, Medium
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(d)
Given speed of sound,
$v=300 \,ms ^{-1}$
And wave equation is
$y=y_0 \sin \left(\frac{2 \pi}{L} x\right) \cdot \sin \left(\frac{2 \pi}{L} x+\frac{\pi}{4}\right)$
So, angular wave number,
$k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{L}$
$\therefore \quad \lambda=L=1.2 \,m$
Frequency of fundamental vibration is
$v=\frac{v}{\lambda}=\frac{300}{12}=250 \,Hz$
So, option $(d)$ is incorrect.
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