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

Explanation

Here, `y_(1)=10sin(3pit+(pi)/(3))`
`therefore`Amplitude of this wave is `A_(1)=10 and y_(2)=5[sin3pit+sqrt(3)cos3pit]`
`=10[(1)/(2)sin3pit+(sqrt(3))/(2)cos3pit]=10["cos"(pi)/(3)sin3pit+"sin"(pi)/(3)cos3pit]`
`=10sin(3pit+(pi)/(3))" "therefore`Amplitude of this wave is `A_(2)=10`
Their corresponding ratio is `(A_(1))/(A_(2))=(10)/(10)=1`