Question

A travelling wave $y=A \sin (k x-\omega t+\theta)$ passes from a heavier string to a lighter string. The reflected wave has amplitude $0.5\, A$. The junction of the strings is at $x=0$. The equation of the reflected wave is:

• A. $y'=0.5 A \sin (k x+\omega t+\theta)$
• B. $y'=-0.5 A \sin (k x+\omega t+\theta)$
• C. $y'=-0.5 A \sin (\omega t-k x-\theta)$
• D. $y'=-0.5 A \sin (k x+\omega t-\theta)$

Answer 1

Answer: (D)

As wave has been reflected from a rarer medium, therefore there is no change in phase. Hence equation for the opposite direction can be written as
$y =0.5\, A\, \sin (-k x-\omega t+\theta)$
$=-0.5\, A\, \sin (k x+\omega t-\theta)$