Two progressive waves of identical amplitude and the same frequency are represented…

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

Problem

Two progressive waves of identical amplitude 3 cm3\,\text{cm} and the same frequency are represented by y1=3sin⁡ωt,y2=3sin⁡(ωt+60∘).y_1 = 3\sin \omega t,\qquad y_2 = 3\sin\bigl(\omega t + 60^{\circ}\bigr). (i) Calculate the amplitude of the resultant wave. (ii) If the intensity of a wave is proportional to the square of its amplitude, determine the intensity of the resultant wave in terms of the intensity I0I_0 of a single wave. (iii) By what factor does the intensity change as compared to I0I_0?

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