Two sinusoidal wave having the same frequency and travelling in the same direction are combined. What is the amplitude of the resultant motion if their amplitudes are 3cm and 4cm and they differ in phase by `pi//2` radian?

Explanation

Amplitude of first shm `= a_1 =4` cm
Amplitude of second shm `= a_2=7 cm`
Phase `= phi=pi/2`
The resultant amplitude =`A=sqrt(a_1^2+a_2^2+2a_1a_2cosphi)`
`sqrt(4^2+7^2+2xx4xx7xx cos pi//2)`
`= sqrt(65) = 08.06 ` cm = 0.0806 m
The phase of the resultant is `theta`
`tan theta= (a_2sinphi)/(a_1+a_2cosphi)`
`= (7 sinpi//2)/(4+7cospi//2)=7/4=1.75`
`= theta = 60^@15.`