Question

Equation of a plane progressive wave is given by $y=A_1\text{sin}\pi (t-\frac{x}{3})$. After reflecting from a rarer medium amplitude of reflected wave becomes $A_2$. The equation of the reflected wave can be

• A. $A_1\text{sin}\pi (t+\frac{x}{3})$
• B. $A_2\text{sin}\pi (t-\frac{k}{3}+1)$
• C. $A_2\text{cos}\pi (t+\frac{x}{3})$
• D. $A_2\text{sin}\pi (t+\frac{x}{3})$

Answer 1

The correct option is D $A_2\text{sin}\pi (t+\frac{x}{3})$

As wave enters from denser to rarer medium therefore, the reflected wave will not be inverted .
Also, the reflected wave will have same speed but propagate in opposite direction to the incident wave.
$\therefore y_r=A_2\text{sin}\pi (t+\frac{x}{3})$