Question

The two waves of same frequency and same amplitude on superposition,produce a resultant disturbance of the same amplitude , the waves differ in phase by

• A. $\pi$
• B. $\frac{2\pi }{3}$
• C. $\frac{\pi }{3}$
• D. $3\pi$

Answer 1

Answer: (B)

$\frac{2\pi }{3}$

Amplitude of resultant disturbance $A_R^2=A_1^2+A_2^2+2A_1{A}_2\cos \theta$
where $\theta$ is the phase difference between two waves.
Given : $A_1=A_2=A$
Also, resultant amplitude $A_R=A$
$\therefore$ $A^2=A^2+A^2+2A^2\cos \theta$
Or $\cos \theta =-\frac{1}{2}$
$⟹\theta =\frac{2\pi }{3}$