Question

For given shape of wave at time $t=t_0$, velocity of particle at $x=x_0$ is twice the wave velocity of given transverse wave. Find the slope of wave at $x=x_0$.

• A. $2$
• B. $-2$
• C. $1$
• D. $-1$

Answer 1

The correct option is B $-2$

The particle velocity$\left(v_P\right)$ and wave velocity$\left(v\right)$ is related as,
$\Rightarrow v_P=-v\times \frac{dy}{dx}....\left(i\right)$
where$\frac{dy}{dx}=$slope of wave at a given position

At position $x=x_0$,
$\Rightarrow v_P=2\times v$
Comparing it with equation $\left(i\right)$ gives,
$\Rightarrow -\frac{dy}{dx}=2$
$\Rightarrow \text{slope of wave}=\frac{dy}{dx}=-2$