Three component sinusoidal waves progressing in the same directions along the same path have the same period but their amplitudes are `A, A/2 and A/3.` The phases of the variation at any position x on their path at time `t = 0 are 0, -pi/2 and -pi` respectively. Find the amplitude and phase of the resultant wave.

Explanation

Phasor diagram Wave || `phi_2 =pi/2`

`A_R =sqrt(((2y_1)/3)^2 +(y_1/2)^2) =y_1sqrt(4/9 +1/4) =5/6 y_1`
`phi_R = tan^(-1) ((y_1//2)/(2y_1 //3)) = tan^(-1) (3//4) =37^@`
The phase constant of the resultant wave with respect to first wave is `37^0`.