Question

The equation of a wave travelling on a string is given by $y=8\sin \left[\right(5m^{-1})x-(4s^{-1}\left)t\right]$. Then,

• A. velocity of the wave is $0.8m/s$
• B. the displacement of a particle of the string at $t=0$ and $x=\frac{\pi }{30}m$ from the mean position is $4m$
• C. the displacement of a particle from the mean position at $t=0$, and $x=\frac{\pi }{30}m$ is $8m$
• D. velocity of the wave is $8m/s$

Answer 1

Answer: (A), (B)

The correct options are
A velocity of the wave is $0.8m/s$
B the displacement of a particle of the string at $t=0$ and $x=\frac{\pi }{30}m$ from the mean position is $4m$

$y=A\sin (kx-wt)$
Comparing with the given equation,
Velocity $=\frac{w}{k}=\frac{4}{5}=0.8\frac{m}{s}$
At, $t=0$ and $x=30m$
$y=8\sin \left(150\right)=\frac{8}{2}=4m$