An oscillation is superposition of three harmonic oscillations and decribed by the equation `x=A sin 2pi upsilon_(1)` where A changes with time according to `A=A_(0)(1+cos 2pi upsilon_(2)t)` with `A_0` to be constant. The frequencies of pure harmonic oscillations forming this oscillation are

Options

A. (a)`upsilon_(1),upsilon_(2),upsilon_(1)-upsilon_(2)`
B. (b)`upsilon_(1),upsilon_(2),upsilon_(1)+upsilon_(2)`
C. (c)`upsilon_(1),upsilon_(1)+upsilon_(2),upsilon_(1)-upsilon_(2)`
D. (d)`upsilon_(2),upsilon_(1)+upsilon_(2),upsilon_(1)-upsilon_(2)`

Answer

B

Explanation

`x = A_(0)(1+cos2pigamma_(2)t) sin (pigamma_(1))`
`= A_(0)[sin 2pigamma_(1)t + cos 2pigamma_(2)t + sin 2pigamma_(1)t]`
`= A_(0)[sin 2pigamma_(1)t + 1/2 sin (2pi(gamma_(1) + gamma_(2))t - 1/2 sin (2pi(gamma_(1) - gamma_(2)t)]`
Required ratio `= v_(1) : (v_(1) - v_(2)) : (v_(1) + v_(2))`