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

MCQ

Two waves having equations

${x_1} = a\sin (\omega \,t + {\phi _1})$, ${x_2} = a\sin \,(\omega \,t + {\phi _2})$

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
(b) Superposition of waves does not alter the frequency of resultant wave and resultant amplitude

$\Rightarrow$ ${a^2} = {a^2} + {a^2} + 2{a^2}\cos \phi = 2{a^2}(1 + \cos \phi )$

$\Rightarrow$ $\cos \phi = - 1/2 = \cos 2\pi /3$ $\therefore$ $\phi = 2\pi /3$

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