Wave Mechanics Question 710

Question: $ y=a\cos (kx+\omega t) $ superimposes on another wave giving a stationary wave having node at x = 0. What is the equation of the other wave

[BHU 1998; DPMT 2000]

Options:

A) $ -a\cos (kx+\omega t) $

B) $ a\cos (kx-\omega t) $

C) $ -a\cos (kx-\omega t) $

D) $ -a\sin (kx+\omega t) $

Show Answer

Answer:

Correct Answer: C

Solution:

$ a\cos (kx+\omega ,t) $ hence $ {y _{reflected}}=a\cos (-kx+\omega ,t+\pi )=-a\cos (kx-\omega ,t) $