Physics · JEE | WAVES

Two harmonic travelling waves are given by \( y_1(x, t) = a \sin(kx - \omega t) \) and \( y_2(x, t) = a \sin(kx - \omega t + \phi) \). The amplitude of the resultant wave formed by their superposition is given by:

1. A
   \( a \cos(\frac{\phi}{2}) \)
2. B
   \( 2a \cos(\frac{\phi}{2}) \)
3. C
   \( a \sin(\frac{\phi}{2}) \)
4. D
   \( 2a \sin(\frac{\phi}{2}) \)