The displacement equations of two interfering waves are given by y 1 = 10 sin ω t + π 3 cm , y 2 = 5 sin ω t + 3 cos ω t cm respectively. The amplitude of the resultant wave is _____ cm .

Step-by-step solution

Displacement equation of second wave can be written as, y 2 = 5 sin ω t + 3 cos ω t = 10 sin ω t × 1 2 + 3 2 × cos ω t = 10 sin ω t × cos π 3 + sin π 3 × cos ω t = 10 sin ω t + π 3 As we can see, the phase difference between the waves is 0 . Therefore, resultant amplitude will be sum of the amplitudes of the waves. So A = A 1 + A 2 = 10   cm + 10   cm = 20   cm