The displacement of a particle executing periodic motion is given by :
$y = 4cos^2\,(t/2)sin\,(1000t)$
This expression may be considered to be a result of superposition of
$y = 4cos^2\,(t/2)sin\,(1000t)$
This expression may be considered to be a result of superposition of
Diffcult
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$y=4 \cos ^{2}(t / 2) \sin (1000 t)$
$=2\left[2 \cos ^{2}(t / 2) \sin (1000 t)\right]$
$=2(1+\cos t) \sin (1000 t)$
$=2 \sin (1000 t)+2 \sin (1000 t) \cos t$
$=2 \sin (1000 t)+\sin (1001 t)+\sin (999 t)$
i.e., the given wave represents the superposition of three waves.
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