Waves question for NEET / JEE Main, with solution

Answer: (A) $8$ m/s

Concept. For $y = A\sin(\omega t - kx)$ the wave speed is $v = \dfrac{\omega}{k}$.

Step 1. Read off. $\omega = 4\pi$ rad/s, $k = 0.5\pi$ rad/m.

Step 2. Speed.
$$v = \frac{4\pi}{0.5\pi} = 8\ \text{m/s}$$

Answer. $8$ m/s (Option A).

Solution by Sreeraj P, M.Sc Physics