Question

Two harmonic waves $y_1=a\cdot \sin (kx-\omega t)$ and $y_2=a\cdot \sin (kx-\omega t+\varphi )$ are moving in the same direction, if both the waves are superimposed then the initial phase angle of the resultant wave is:

• (A) $\varphi$
• (B) $\frac{\varphi }{2}$
• (C) $\frac{\varphi }{4}$
• (D) None of these

Answer 1

The Correct Option is B

Explanation:
Two harmonic waves are,$y_1=a\cdot \sin (kx-\omega t)$$y_2=a\cdot \sin (kx-\omega t+\varphi )$Where $\varphi =$ phase difference between $y_1$ and $y_2$.By the principle of superposition, the net displacement is given by,$y=2a\cdot \cos \frac{\varphi }{2}\sin (kx-\omega t+\frac{\varphi }{2})\cdots (1)$By equation (1) it is clear that the initial phase angle of the resultant wave is $\frac{\varphi }{2}$.Hence, the correct option is (B).