Question

The equation of a plane progressive wave is $y=0.9sin4\pi [t-\frac{x}{2}]$. When it is reflected at a rigid support, its amplitude becomes $\frac{2}{3}$ of its previous value. The equation of the reflected wave is

• A. $y=0.6sin4\pi [t+\frac{x}{2}]$
• B. $y=-0.6sin4\pi [t+\frac{x}{2}]$
• C. $y=-0.9sin8\pi [t-\frac{x}{2}]$
• D. $y=-0.9sin4\pi [t+\frac{x}{2}]$

Answer 1

The correct option is B $y=-0.6sin4\pi [t+\frac{x}{2}]$

Amplitude of reflected wave $=0.9\times \frac{2}{3}=0.6$
It would travel along negative direction of x-axis , and on reflection at a rigid support, there occurs a phase change of $\pi$.
Hence, the wave equation becomes:
$y=0.6\sin 4\pi (t+\frac{x}{2}+\pi )$
$y=-0.6\sin 4\pi (t+\frac{x}{2})$