The displacement `y` of a particle executing periodic motion is given by `y = 4 cos^(2) ((1)/(2)t) sin(1000t)`
This expression may be considereed to be a result of the superposition of

Options

A. two
B. three
C. four
D. five

Answer

B

Explanation

`y = 4 cos^(2)((t)/(2)) sin 1000 t`
` = 2( 1 + cos t) sin 1000 t`
` = 2 sin 1000 t + 2 cos t sin 1000 t`
` = 2 sin 1000 t + sin (1000 t + t) + sin (1000 t - t)`
`= 2 sin 1000 t + sin 1001 t + sin 999 t`
` = y_(1) + y_(2) + y_(3) = Three waves `