Sound WavesHard
Question
Three simple harmonic waves, identical in frequency n and amplitude A moving in the same direction are superimposed in air such a way, that the first, second and the third wave have the phase angles φ, φ + 
and (φ + π) respectively at a given point P in the superposition.
Then as the waves progress, the superposition will result in
and (φ + π) 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 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
Solution
Since the first wave and the third wave moving in the same direction have the phase angles φ and (φ + π), 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.
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