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 `3A`
B. a stationary simple harmonic wave of amplitude `3A`
C. a stationary 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 angle `phi` and `(phi+ pi)`, they superpose with opposite phase at every point of the vibrating medium and thus cancen out each other, in displacement,velocity and acceleration. They, in effect, destory 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.