Question

Equation of a plane progressive wave is given by $y=0$.$6\sin 2\pi (t-\frac{x}{2})$. On reflection from a denser medium its amplitude becomes $2/3$ of the amplitude of the incident wave. The equation of the reflected wave is

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

Answer 1

The correct option is A $y=-0.4\sin 2\pi (t+\frac{x}{2})$

Step: 1 Find the amplitude of the reflected wave.

Given that equation of progressive wave

$y=0.6\sin 2\pi (t-\frac{x}{2})$

Given that the amplitude becomes $2/3$ of the amplitude of the incident wave, therefore amplitude of reflected wave can be calculated as,

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

Step: 2 Find the equation of the reflected wave.

As we know that when a wave reflects from a denser medium there is a phase change of $\pi$.

So, the equation can be written as,

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

Final Answer: (b)