Wave Motion 5 Question 7
7. The displacement $y$ of a particle executing periodic motion is given by
$$ y=4 \cos ^{2}\left(\frac{1}{2} t\right) \sin (1000 t) $$
This expression may be considered to be a result of the superposition of ………. independent harmonic motions.
$(1992,2 M)$
(a) two
(b) three
(c) four
(d) five
Show Answer
Answer:
Correct Answer: 7. (b)
Solution:
- The given equation can be written as
$$ \begin{aligned} y & =2\left(2 \cos ^{2} \frac{t}{2}\right) \sin (1000 t) \\ y & =2(\cos t+1) \sin (1000 t) \\ & =2 \cos t \sin 1000 t+2 \sin (1000 t) \\ & =\sin (1001 t)+\sin (999 t)+2 \sin (1000 t) \end{aligned} $$
i.e. the given expression is a result of superposition of three independent harmonic motions of angular frequencies 999, 1000 and $1001 rad / s$.
