Equation of a plane progressive wave is given by y=0.6 sin2πt-x2. On reflection from a denser medium, its amplitude becomes  23rd of the amplitude of the incident wave. The equation of the reflected wave is:

1. y=0.6 sin2πt+x2

2. y=-0.4 sin2πt+x2

3. y=0.4 sin2πt+x2

4. y=-0.4 sin2πt-x2

(2) Hint: There would be a phase difference in the incident wave due to reflection.
Step 1: Find the amplitude of the reflected wave.
The amplitude of the reflected wave,
                                             A r=23×A i=23×0.6=0.4 units
Given the equation of the incident wave,
Step 2: Find the equation of the reflected wave.
Equation of the reflected wave is,
                                                                  [At a denser medium, the phase changes by π]
The positive sign is due to the reversal of direction of propagation.
So,                                   yr=-0.4sin2πt+x2                       sinπ+θ=-sinθ