Question

In a sine wave, position of different particles at time t = 0 is shown in figure. The equation for this wave travelling along the positive x – direction can be……..

(A) y = A sin (ωt – kx)

(B) y = A cos (kx – ωt)

(C) y = A cos (ωt – kx)

(D) y = A sin (kx – ωt)

Answer 1

The correct option (D) y = A sin (kx – ωt)

Explanation:

at t = 0, x = 0 & y = 0

hence it has to be sine function. In case of option D.

y = A sin(kx – ωt)

(dy/dt) = – Aω cos(kx – ωt)

& (dy / dx) = kA cos (kx – ωt)

∴ [{dy/dt}/{dy / dx}] = [(– ω)/k] (1)

as wave velocity = V = (ω/k)

hence from(1), (dy/dt) = – V ∙ (dy/dx)

i.e. particle velocity = – (wave velocity) × slope at x = 0, t = 0 slope is

positive, hence particle velocity is in negative y direction.

hence option D is correct choice.