(a) Starting from the expressions and for two sinusoidal waves of the same frequency,…

PHYSICS · Subjective · A Level · Physics · Waves · Waves

Problem

(a) Starting from the expressions

y_1 = a_1\sin \omega t

and

y_2 = a_2\sin( \omega t + \theta)

for two sinusoidal waves of the same frequency, obtain an expression for the amplitude of the resultant wave. (b) Hence derive the relation for the resultant intensity

I

of the two waves in terms of their individual intensities

I_1

and

I_2

and the phase difference

\theta

. (c) For the special case

I_1 = I_2

, calculate

I_{\max}

and

I_{\min}

and comment on the contrast between maxima and minima obtained in this case.

Related theory

Interference
Wave Superposition
Superposition and interference of waves
Principle of superposition
Waves

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