The equation of a transverse wave travelling along a string is $\mathrm{y}(\mathrm{x}, \mathrm{t})=4.0 \sin \left[20 \times 10^{-3} \mathrm{x}+600 \mathrm{t}\right] \mathrm{mm}$, where $x$ is in the mm and $t$ is in second. The velocity of the wave is :

(C) $-30 \mathrm{~m} / \mathrm{s}$

(A) $+30 \mathrm{~m} / \mathrm{s}$

(B) $-60 \mathrm{~m} / \mathrm{s}$

(D) $+60 \mathrm{~m} / \mathrm{s}$

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Waves & Sound

The equation of a transverse wave travelling along a string is

y (x, t) = 4.0 sin [20 \times 1 0^{- 3} x + 600 t] mm

, where

x

is in the mm and

t

is in second. The velocity of the wave is :

Answer: (C)

The equation

y = 4.0 sin [20 \times 1 0^{- 3} x + 600 t]

mm has the form

y = A sin (k x + ω t)

, with

ω = 600 rad/s, k = 20 \times 1 0^{- 3} rad/mm = 20 rad/m

The wave speed is

v = \frac{ω}{k} = \frac{600}{20} = 30 m/s

Since the phase is

(k x + ω t)

rather than

(k x - ω t)

, the wave travels in the

- x

direction, so

v = - 30 m/s

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Single correct option