Question

If 2 waves of same frequency and same amplitude on superposition, produce a resultant disturbance of the same amplitude, the waves differ in phase by

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

Answer 1

Answer: (B)

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

Let the amplitude of each wave be $A$ i.e. $A_1=A_2=A$
Thus amplitude of resultant wave $A_R=A$
Using $A_R^2=A_1^2+A_2^2+2A_1{A}_2\cos \theta$
$\therefore$ $A^2=A^2+A^2+2A^2\cos \theta$
Or $\cos \theta =-0.5$
$⟹\theta =\frac{2\pi }{3}$