The displacement of a particle as a function of time t is given by y
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y = 4 cos2 (1/2 t) sin (1000 t)
= 2 x 2 cos2(t/2)sin (1000 t)
= 2 x (1 + cos t) sin (1000 t)
= 2 sin (1000 t) + 2 cos t sin (1000 t)
= 2 sin (1000 t) + sin [(1000+1)t] +sin [(1000−1)t]
= 2 sin (1000 t) + sin (1001)t +sin (999)t
= y1 + y2 + y3
As the above expression involves three different waves the displacement given is a result of superposition of three different waves
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