Q. 21

# The displacement

Answer :

Given:

Displacement equation of an elastic wave y = 3sinωt + 4cosωt

Let 3 = Acosθ and 4 = Asinθ, then the equation for displacement becomes: by using the property we have ,  Which is the equation for a simple harmonic wave with amplitude A and phase difference θ. For θ we have   For amplitude A, squaring and adding 3 = Acosθ and 4 = Asinθ, we have   And Therefore, the equation for the wave becomes with its amplitude being 5 m.

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