The equation of displacement of two waves are given as
` y_(1) = 10 sin( 3 pi t + (pi)/(3)) , y_(2) = 5 [ sin 3 pi t + sqrt(3) cos 3 pi t]`
Then what is the ratio of their amplitudes

Options

A. `2 : 1`
B. `1 : 1`
C. `1 : 2`
D. None of these

Answer

B

Explanation

`y_(1) = 10 sin (3pi t + (pi)/(3))`….(1)
`y_(2) = 5(sin 3pi t + sqrt3 cos 3pi t)`
`= 5 xx 2 [(1)/(2) sin 3pi t + (sqrt3)/(2) cos 3pi t]`
`= 10 [cos ((pi)/(3)) sin 3pi t + sin ((pi)/(3)) cos 3pi t]`
`= 10 [sin (3pit + (pi)/(3))]`
`[ :' sin (A + B) = sin A cos B + cos A sin B]`
From (1) and (2), the ratio of the amplitudes of (1) and (2) is `(10)/(10) = 1 : 1`