Question

For a plane progressive wave represented by, $y=5\sin (100\pi t-0.4\pi x)$, what is the wave velocity (in $\text{m/s}$)?

• A. $350$
• B. $250$
• C. $200$
• D. $180$

Answer 1

The correct option is B $250$

Given
$y=5\sin (100\pi t-0.4\pi x)$
Comparing with wave equation format,
$y=A\sin (\omega t-kx)$
We get $\omega =100\pi ;k=0.4\pi$
Since $\omega =2\pi f$
$\Rightarrow 2\pi f=100\pi$
$\Rightarrow f=50\text{Hz}$
and,
$k=\frac{2\pi }{\lambda }$
$\Rightarrow \frac{2\pi }{\lambda }=0.4\pi$
$\lambda =5\text{m}$
Velocity of a wave is given by $v=f\lambda$
$\Rightarrow v=50\times 5$
$\therefore v=250\text{m/s}$