Question

A progressive wave is represented by $y=5\sin (100\pi t-2\pi x)$ where $x$ and $y$ are in $m$ and $t$ is in $s$. The maximum particle velocity is :

• A. $100\pi m{s}^{-1}$
• B. $200\pi m{s}^{-1}$
• C. $400\pi m{s}^{-1}$
• D. $500\pi m{s}^{-1}$

Answer 1

The correct option is D $500\pi m{s}^{-1}$

the given progressive wave is
$y=5\sin (100\pi t-2\pi x)$
particle velocity, ${\nu }_p=\frac{dy}{dt}=500\pi \sin (100\pi t-2x)$
${\nu }_{(}{p}_{max})=500m{s}^{-1}$