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JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Waves & Sound

In the wave equation

y = 0.5 sin \frac{2 π}{λ} (400 t - x) m

the velocity of the wave will be :

(A) $200 m / s$
(B) $2002 m / s$
(C) $400 m / s$ ✓ Correct
(D) $4002 m / s$

Answer: (C)

Solution

The wave equation is

y = 0.5 sin (\frac{2 π}{λ} (400 t - x))

. Comparing with

y = A sin (ω t - k x)

, we have

ω = \frac{2 π \cdot 400}{λ}

and

k = \frac{2 π}{λ}

. Wave velocity

v = \frac{ω}{k} = \frac{2 π \cdot 400/ λ}{2 π / λ} = 400

m/s.

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Single correct option

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