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Q.
If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude the waves differ in phase by
Waves
Solution:
Let $A$ and $v$ be the amplitude and frequency of each wave differing in phase by $\phi .$ Then
and $y_{2}=A \sin (k x-2 \pi v t+\phi)$
According to the principle of superposition, the resultant wave is
$y=y_{1}+y_{2}=A \sin (k x-2 \pi v t)+A \sin (k x-2 \pi v t+\phi)$
or $\,\,\,y=\left(2 A \cos \frac{\phi}{2}\right) \sin \left(k x-2 \pi v t+\frac{\phi}{2}\right)$
But as per question $2 A \cos \frac{\phi}{2}=A$
or $\cos \frac{\phi}{2}=\frac{1}{2}$ or $\frac{\phi}{2}=\frac{\pi}{3}$
or $\phi=\frac{2 \pi}{3}$