Question

Equation of a plane progressive wave is given by $y=0.5\text{sin}3\pi (t-\frac{x}{3})$. On reflection from a denser medium its amplitude becomes $\frac{2}{5}$ of the amplitude of the incident wave. The equation of the reflected wave is

• A. $0.2\text{sin}\left(\pi \right(3t+x\left)\right)$
• B. $-0.2\text{sin}(3\pi t+\pi x)$
• C. $0.5\text{sin}(\pi t+x)$
• D. $0.2\text{sin}\left(\pi \right(3t-x\left)\right)$

Answer 1

The correct option is B $-0.2\text{sin}(3\pi t+\pi x)$

Given: $y_i=0.5\text{sin}3\pi (t-\frac{x}{3})$
We know, when waves propagate from rarere to denser medium there is phase change of $\pi$ w.r.t. incident wave.
Also, direction of propagation of reflected wave will, be opposite to the incident wave
$\therefore y_r=A_r\text{sin}(3\pi (t+\frac{x}{3})+\pi )$
Given $A_r=\frac{2}{5}\times 0.5$
$\therefore y_r=0.2\text{sin}(3\pi (t+\frac{x}{3})+\pi )$
$=0.2\text{sin}(3\pi t+\pi x+\pi )$
$=-0.2\text{sin}\left(\pi \right(3t+x\left)\right)$