Q 11-14-032JEE MainJEE Main 2026 (2 Apr, Shift 1)Easy
The equation of a plane progressive wave is given by $y=5\cos\pi\left(200t-\dfrac{x}{150}\right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ______ m/s.
Answer: (D) $300$
Compare with $y=A\cos(\omega t-kx)$: $\omega=200\pi$ rad/s and $k=\dfrac{\pi}{150}$ cm$^{-1}$.
$$v=\frac{\omega}{k}=\frac{200\pi}{\pi/150}=30000\ \text{cm/s}=300\ \text{m/s}$$
Solution by Sreeraj P, M.Sc Physics