Question

If two waves of same frequency and same amplitude on superimposition produce a resultant wave of the same amplitude, the wave differs in phase by

• A. $\frac{\pi }{5}$
• B. $\frac{2\pi }{3}$
• C. $\frac{\pi }{4}$
• D. zero

Answer 1

Answer: (B)

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

Let $\overrightarrow{Y_1}\&\overrightarrow{Y_2}$ be the waves which differ in phase by $\theta$

Since, superposition of waves follows laws of vector addition $\overrightarrow{Y}=\overrightarrow{Y_1}+\overrightarrow{Y_2}$

Also $\left|\overrightarrow{Y}\right|=\left|\overrightarrow{Y_1}\right|=\left|\overrightarrow{Y_2}\right|=y$

$Y^2=Y_1^2+Y_2^2+2Y_1{Y}_2\cos \theta$

$y^2=y^2+y^2+2y^2\cos \theta$

$\cos \theta =\frac{-1}{2}$

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