Two harmonic travelling waves are described by the equations `y_(1)=a sin(kx-omega t)`  and `y_(2)=a sin(-kx+omega t+phi)`. The amplitude of the superimposed wave is 

Options

A. `2 a cos (phi)/(2)`
B. `2a sin phi`
C. `2a cos phi`
D. `2 a sin (phi)/(2)`

Answer

D

Explanation

`y_1 = a sin (kx- omegat)" "…(1)`
`y_2 = a sin (-kx + omegat + phi)" "…(2)`
On adding (1) and (2),
`y_1 + y_2 = 2a sin (((kx- omega t + kx+ omega t + phi))/(2))`
`cos ((kx-omegat + kx - omega t - phi)/(2))`
`=2a sin (phi/2) cos ( (2 (kx + omega t) - phi)/(2) )`
Amplitude, A `( phi)` is a function of phase difference `phi` between consistutent of waves.
`therefore (phi) =2 a sin (phi//2)`