Question

The equation of a plane progressive wave is $y=0.9\sin 4\pi [t-\frac{x}{2}]$ , when it is reflected at a rigid support, its amplitude becomes $2/3$ of its previous value. The equation
of the reflected wave is :

• A. $y=0.9\sin 4\pi [t+\frac{x}{2}]$
• B. $y=-0.6\sin 4\pi [t+\frac{x}{2}]$
• C. $y=0.9\sin 8\pi [t-\frac{x}{2}]$
• D. $y=0.6\sin 4\pi [t+\frac{x}{2}]$

Answer 1

The correct option is B $y=-0.6\sin 4\pi [t+\frac{x}{2}]$

$y=0.9\sin 4\pi (t-\frac{x}{2})$
Reflected wave equation will be opposite in direction and of amplitude $\frac{2}{3}\times 0.9=0.6$ and amplitude will be negative of incident wave.
So, $y_{reflected}=-0.6\sin 4\pi (t+\frac{x}{2}).$