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Resultant Amplitude and Intensity

Let us consider two waves that have the same frequency but have a certain fixed (constant) phase difference between them. Their super position is shown in Fig. 6.
Fig. 6
Let the two waves are:
y1 = a1 sin ωt and y2 = a2 sin (ωt + φ)
where a1a2 = individual amplitudes, φ = phase difference between the waves at an instant when they are meeting a point.
Resultant amplitude The resultant wave can be written as y = A sin (ωt + θ), where A = resultant amplitude 94775.png
Resultant intensity As we know intensity ∝ (amplitude)2.
⇒ I1 = ka21i2 = ka22 and I2 = kA2 and (k is a proportionality constant). Resultant intensity,
For two identical source I1 = I2 = I0

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