The equations of displacement of two waves are
`y_(1)=10"sin"(3pit+pi//3)`
and `y_(2)=5["sin"3pit+sqrt(3)"cos"3pit]`
What is the ratio of their amplitude ?

Answer

`1:1`

Explanation

`Y_(1)=10sin(3pit+pi//4)`
`Y_(2)=5sin3pit+5sqrt3cos3pi=5sin3pit+5sqrt3sin((pi)/(2)+3pit)`
Applying phasor method `Y_(2)=Asin(3pit+phi)`
Where `A=sqrt((5)^(2)+(5sqrt3)^(2)+2(5)(5sqrt3)("cos"(pi)/(2)))=10`
So, the ratio of amplitudes is 10 : 10, i.e., 1 : 1.