A travelling wave `y=Asin(kx-omegat+theta)` passes from a heavier string to a lighter string. The reflected wave has amplitude `0.5A`. The junction of the string is at `x=0` The equation of the reflected is :

Options

A. `y'=0.5 A sin (kx+omegat+theta)`
B. `y'=-0.5 A sin (kx+omega t+theta)`
C. `y'=-0.5 A sin (omegat-kx-theta)`
D. `y'=0.5 A sin (kx+omegat-theta)`

Answer

D

Explanation

As wave has been reflected from a rarer medium, therefore there is no change in phase. Hence equation for the opposite direction can be written as
`y=0.5Asin (-kx-omegat+theta)`
`=-0.5A sin (kx+omegat -theta)`