Question

Two waves of the same frequency and same amplitude, on superimposition, produced a resultant disturbance of the same amplitude. The waves differ in phase by

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

Answer 1

Answer: (B)

Amplitude of resultant wave is
$A^{2}=A_{1}^{2}+A_{2}^{2}+2A_{1}A_{2}cos \theta $

Given, $A=A_{1}=A_{2}=a$ (let)
$a^{2}=a^{2}+a^{2}+2a^{2}cos \theta $
$cos \theta =-\frac{1}{2}$
$\theta =\frac{2 \pi }{3}$