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
AIPMT 2001, Medium
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(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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