Question

Two waves having equations
$x_{1}=a \sin \left(\omega t+\varphi_{1}\right), x_{2}=a \sin \left(\omega t+\varphi_{2}\right)$
If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is

• A. $\frac{\pi}{6}$
• B. $\frac{2 \pi}{3}$
• C. $\frac{\pi}{4}$
• D. $\frac{\pi}{3}$

Answer 1

Answer: (B)

Superposition of waves does not alter the frequency of resultant wave and resultant amplitude
$\Rightarrow a^{2}=a^{2}+a^{2}+2 a^{2} \cos \varphi=2 a^{2}(1+\cos \varphi)$
$\Rightarrow \cos \varphi=-1 / 2=\cos 2 \pi / 3$
$\therefore \varphi=2 \pi / 3$