Two waves having equations x_1=a ( t+ _1 ), x_2=a ( t+ _2 ) If in… - Vidyadip

MCQ

Two waves having equations
$ x_1=a \sin \left(\omega t+\phi_1\right), x_2=a \sin \left(\omega t+\phi_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
$\frac{\pi}{6}$
✓
$\frac{2 \pi}{3}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{3}$

✓

Answer

Correct option: B.

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

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

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