Three simple harmonic waves , identical in frequency `n` and amplitude `A` moving in the same direction are superimposed in air in such a way , that the first , second and the third wave have the phase angles `phi , phi + ( pi//2) and (phi + pi)`, respectively at a given point `P` in the superposition
Then as the waves progress , the superposition will result in

Options

A. a periodic , non - simple harmonic wave of amplitude `3 A`
B. a stationary simple harmonic wave of amplitude ` 3 A`
C. a simple harmonic progressive wave of amplitude `A`
D. the velocity of the superposed resultant wave will be the same as the velocity of each wave

Answer

C, D

Explanation

Since the first wave and the third wave moving in the same direction have the phase angles `phi and ( phi + pi)` , they superpose with opposite phase at every point of the vibrating medium and thus cancel out each other , in displacement , velocity , and acceleration. They in effect , destroy each other out . Hence we are left with only the second wave which progresses as a simple harmonic wave of amplitude `A`. The velocity of this wave is the same as if it were moving alone.