The displacement $y$ of a particle executing periodic motion is given by $y = 4 c o s^{2} (t) s i n (1000 t)$ . this expression may be considered to be a result of the superposition of waves

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Solution

The correct option is C 3
$y = 4 c o s^{2} (t) s i n (1000 t)$

$= 2 (2 c o s^{2} t) s i n 1000 t = 2 (1 + c o s 2 t) s i n 1000 t = 2 s i n 1000 t + 2 c o s (2 t) s i n (1000 t) = s i n 1000 t + s i n (1002 t) + s i n (998 t) = y_{1} + y_{2} + y_{3}$

Therefore, superposition of three waves.

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