Question

Equation of a plane progressive wave is given by y = $0.6.\sin 2\pi\left( t - \frac{x}{2} \right)$. On reflection from a denser medium its amplitude becomes $\frac{2}{3}$ of the amplitude of the incident wave. The equation of the reflected wave is.

• A. $y = 0.6\sin 2\pi\left( t + \frac{x}{2} \right)$
• B. $y = - 0.4\sin 2\pi\left( t + \frac{x}{2} \right)$
• C. $y = 0.4\sin 2\pi\left( t + \frac{x}{2} \right)$
• D. $y = - 0.4\sin 2\pi\left( t - \frac{x}{2} \right)$

Answer 1

Answer: (B)

$y = - 0.4\sin 2\pi\left( t + \frac{x}{2} \right)$

Answer 2

Amplitude of reflected wave

$= \frac{2}{3} \times 0.6 = 0.4$

On reflection from a denser medium there is phase change of $\pi.$

$\therefore$Equations of reflected wave is

$y = 0.4\sin 2\pi\left( t + \frac{\pi}{2} + \pi \right)$

$= - 0.4\sin 2\pi\left( t + \frac{x}{2} \right)$