Question

Two waves having equation $x_1=a \sin(\omega t-kx+\phi_1),$ $x_2=a \sin (\omega t-kx +\phi_2)$ If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the 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)

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

Answer 2

Resultant amplitude = $2a (1 + \cos \phi)$ = a
$\therefore (1+ \cos \phi)=1/2; \cos\phi=-\frac{1}{2}; \phi=\frac{2\pi}{3}$.