The equation of a plane progressive wave is given by $y=5 \cos \pi\left(200 t-\frac{x}{150}\right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ____ $\mathrm{m} / \mathrm{s}$

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Waves & Sound

The equation of a plane progressive wave is given by

y = 5 cos π (200 t - \frac{x}{150})

where

x

and

y

are in cm and

t

is in second. The velocity of the wave is ____

m / s

Answer: (D)

Writing the wave as

y = 5 cos (200 π t - \frac{π}{150} x)

, the angular frequency is

ω = 200 π s^{- 1}

and the wave number is

k = \frac{π}{150} c m^{- 1}

. The wave speed is

v = \frac{ω}{k} = \frac{200 π}{π /150} = 200 \times 150 = 3 \times 1 0^{4}

cm/s. The velocity of the wave is

300 m/s

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Single correct option