Question

If two waves of same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude, the wave differ in phase by :

• A. $\pi$
• B. zero
• C. $\pi /3$
• D. $2\pi /3$

Answer 1

Answer: (D)

$2\pi /3$

Resultant amplitude due to superposition of two waves with phase difference $\varphi$ is given by

$A^2=A_1^2+A_2^2+2A_1{A}_{2}cos\varphi$

It is given that $A_1=A_2=A$

Thus $A^2=A^2+A^2+2A^{2}cos\varphi$

$⟹cos\varphi =-\frac{1}{2}$

$⟹\varphi =\frac{2\pi }{3}$