A plane wave `y =a sin (bx + ct)` is incident on a surface. Equation of the reflected wave is `y' = a' sin(ct-bx)`. Which of the following statements is not correct ?

Options

A. The wave is incident normally on the surface
B. Reflecting surface is `y - z `plane
C. Medium , in which incident wave is travelling , is denser than the other medium
D. `a'` cannot be greater than `a`

Answer

A, B, C, D

Explanation

If a wave is incident normally on a surface then it gets reflected back to its original path . The incident wave is travelling along negative ` x - direction` and reflected wave is travelling along positive ` x - direction`. Hence , the wave is incident normally on the surface . Therefore, option `(a)` is correct.
The equation of the reflected wave will be ` y' = a' sin ( ct - bx + phi)` only when the reflecting surface is ` x = 0 ` plane , i.e., ` y - z` plane.
Hence option `(b)` is correct.
Since , `phi` is equal to zero , it means , no phase change takes place at the reflecting surface . It is possible only when the reflecting surface . It is possible only when the reflecting surface is boundary of a rarer medium . It means wave is travelling in a denser medium relative to the other medium . Hence `( c)` is also correct .
If the reflecting surface is perfectly elastic when whole of the incident energy gets reflected back. In that case `a' ` will be equal to `a`. But if a part of wave is refracted into the other medium , then the the amplitude of oscillations for the reflected wave will be less than that for incident wave . It implies that `a'` can never be greater than `a`. Hence , option `(d)` is also correct.