Question

A wave travelling along positive x-axis is given by $=A\sin (\omega t-kx)$. If it is reflected from a rigid boundary such that $80$% amplitude is reflected, then equation of reflected wave is

• A. $y=A\sin (\omega t+0.8kx)$
• B. $y=-0.8A\sin (\omega t+kx)$
• C. $y=A\sin (\omega t+kx)$
• D. $y=0.8A\sin (\omega t+kx)$

Answer 1

Answer: (B)

$y=-0.8A\sin (\omega t+kx)$

On getting reflected from a rigid boundary the wave suffers an additional phase change of $\pi$.
Hence, if $y_{incident}=A\sin (\omega t-kx)$
Then, $y_{reflected}=\left(0.8A\right)\sin (\omega t-k(-x)+\pi )=-0.8A\sin (\omega t+kx)$