Question

The displacement $y$ of a particle in a medium can be expressed as:

$y=10^{-6} \sin (100 t+20 x+\pi / 4) m ,$ where $t$ is in second and

$x$ in meter. The speed of the wave is

• A. 2000 m / s
• B. 5 m / s
• C. 20 m / s
• D. $5 \pi m / s$.

Answer 1

Answer: (B)

Given wave equation :
$y=10^{-6} \sin \left(100 t+20 x+\frac{\pi}{4}\right) m$
Standard equation $: y=a \sin (\omega t+k x+\phi)$
Compare the two
$\therefore \omega=100$ and $k=20$
$\therefore \frac{\omega}{k}=\frac{100}{20} $
$\Rightarrow \frac{2 \pi n}{2 \pi / \lambda}=n \lambda=v=5$
$\therefore \quad v=5 m / s$