Question

Shape of a transverse wave at time $t=t_0$ is shown in the figure given below.

At $x=x_0$ and time $t=t_0$, slope of the wave curve is $5$. Find the ratio of particle velocity to the wave velocity at $x=x_0$.

• A. $-5:1$
• B. $1:-5$
• C. $5:1$
• D. $1:5$

Answer 1

The correct option is A $-5:1$

We know that,
$\text{Particle velocity}=-\text{wave velocity}\times \text{slope of the wave}$
$\Rightarrow \frac{\text{Particle velocity}}{\text{wave velocity}}=-\text{slope of the wave}$
since, slope of wave at $x=x_0,t=t_0$ is $5$
$\therefore \frac{\text{Particle velocity}}{\text{wave velocity}}=-5$