Three component sinusoidal waves progressing in the same directions along the same path have the same period byt 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.

Three component sinusoidal waves progressing in the same directions al

1.	Three component sinusoidal waves progressing in the same directions along the same path have the same period byt 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.
Answer» Solution :Resultant AMPLITUDE `A_r = SQRT ((2A)/3)^2 + (A/2)^2 ` `= 5/6 A ` `tan phi = - (A//2)/(2A//3) = -3/4` or`phi = tan ^-1 (3//4)` .