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 .

Question

TestHub · Accepted Answer

Displacement equation of second wave can be written as, $y_{2} = 5 (\sin ω t + \sqrt{3} \cos ω t) = 10 (\sin ω t \times \frac{1}{2} + \frac{\sqrt{3}}{2} \times \cos ω t) = 10 (\sin ω t \times \cos \frac{π}{3} + \sin \frac{π}{3} \times \cos ω t)$

$= 10 \sin (ω t + \frac{π}{3})$

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 $A = A_{1} + A_{2} = 10 cm + 10 cm = 20 cm$

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