Question

A wave, $y=2\text{sin}(\pi t+x+\frac{\pi }{6})$ is propagating on a stretched string fixed at one end. The equation of reflected wave can be given as

• A. $-2\text{sin}(\pi t-x+\frac{\pi }{6})$
• B. $-3\text{sin}(\pi t-x+\frac{\pi }{6})$
• C. $3\text{sin}(\pi t-x+\frac{\pi }{6})$
• D. $2\text{sin}(\pi t-x+\frac{\pi }{6})$

Answer 1

The correct option is A $-2\text{sin}(\pi t-x+\frac{\pi }{6})$

As we know that, when reflection takes place from fixed end reflected wave has phase difference of $\pi$ with respect to incident wave.
Also, direction of propagation of reflected wave is opposite to the incident wave.
$\therefore$ Equation of reflected wave can be given as
$y_r=2\text{sin}(\pi t-x+\frac{\pi }{6}+\pi )$
$=-2\text{sin}(\pi t-x+\frac{\pi }{6})$