Question

A standing wave set up in a medium is $y=4\cos \left(\frac{\pi x}{3}\right)\sin 40\pi t$ where $x,y$ are in $cm$ and $t$ in $sec.$ The velocity of medium particle at $x=6cm$ at $t=\frac{1}{8}sec$ is

• A. $40\pi cm/s$
• B. $80\pi cm/s$
• C. $120\pi cm/s$
• D. $-160\pi cm/s$

Answer 1

Answer: (D)

$-160\pi cm/s$

The velocity of medium particle is given as $v=dy/dt=40\pi \times 4\cos (\frac{x\pi }{3})\cos 40\pi t$

At $x=6cm$, $t=1/8sec$, $v=160\pi \cos \left(2\pi \right)\cos \left(5\pi \right)=-160\pi cm/s$