Question

Two waves of same amplitude and frequency and travelling in same direction are superimposed each other to give rise to a resultant wave of amplitude $\sqrt{(}2)A$. The phase difference between the waves are

• A. $\theta =\pi$
• B. $\theta =\pi /2$
• C. $\theta =3\pi /2$
• D. $\theta =\pi /4$

Answer 1

The correct option is B $\theta =\pi /2$

The resultant of two waves is given by $R^2=A^2+B^2+2ABcos\theta ;\theta$ is the phase difference and A and B are the amplitudes of the individual waves.
Since both the waves are identical, their amplitudes are equal
Since $R^2=2A^2$, Substituting, we get $\theta =\pi /2$
The correct option is (b)