A wave travelling along positive $X$-axis is given by $y = A \sin(\omega t - kx)$. If it is reflected from a…

A wave travelling along positive $X$-axis is given by $y = A \sin(\omega t - kx)$. If it is reflected from a rigid boundary such that $80\%$ amplitude is reflected, then equation of reflected wave is
  1. $y = A \sin(\omega t + 0.8 kx)$
  2. $y = - 0.8 A \sin(\omega t + kx)$
  3. $y = A \sin(\omega t + kx)$
  4. $y = 0.8 A \sin(\omega t + kx)$

Solution

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

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