Question

The equation of a plane progressive wave is $y=0.09\text{sin}8\pi (t-\frac{x}{20})$. When it is reflected at rigid support, its amplitude become ${\frac{2}{3}}^{rd}$ of its previous value. Then the equation of the reflected wave is

• A. $y=0.09\sin 8\pi (t-\frac{x}{20})$
• B. $y=0.09\sin 8\pi (t+\frac{x}{20})$
• C. $y=0.06\sin 8\pi (t+\frac{x}{20})$
• D. $y=-0.06\sin 8\pi (t+\frac{x}{20})$

Answer 1

The correct option is D $y=-0.06\sin 8\pi (t+\frac{x}{20})$

When wave gets reflected at rigid support, it undergoes a phase change of $\pi$ and travels in opposite direction but its wavenumber and angular frequency remain same.
It is given, amplitude of reflected wave become ${\frac{2}{3}}^{rd}$ of its previous value.
So, amplitude of reflected wave, $A_r=\frac{2}{3}\times 0.09=0.06\text{cm}$
Hence,
Reflected wave equation is
$y=0.06\sin 8\pi (t+\frac{x}{20}+\pi )$
$\Rightarrow y=-0.06\sin 8\pi (t+\frac{x}{20})$