A harmonic vibration has an amplitude that varies as a, Ask an Expert

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A harmonic vibration has an amplitude that varies as a cosine function along the x-direction such that

y=a cos kx. sin ωt

Show that if another harmonic vibration of same frequency and equal amplitude displaced in space phase and time phase by a quarter wavelength is added to the first vibration, the resultant vibration will represent a traveling wave with a propagation velocity equal to c=ω/k.

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