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?

Two sinusoidal wave having the same frequency and travelling in the sa

1.	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?
Answer» SOLUTION :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.`