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Question

Physics Question on wave interference

If two waves of same amplitude A each produce Maximum Marks 600 a resultant wave of amplitude equal to one of its wave, then the phase difference between them will be

A

60∘C60^{\circ} C

B

90∘C90^{\circ} C

C

120∘C120^{\circ} C

D

180∘C180^{\circ} C

Answer

120∘C120^{\circ} C

Explanation

Solution

Let θ\theta be the phase difference between two waves According to the principle of superposition, the amplitude of a resultant wave is R=[A12+A22+2A1A2 cos ϕ]1/2R=[A^{2}_{1}+A^{2}_{2}+2A_{1}A_{2}\,cos\,\phi]^{1/2} As per question A=[A2+A2+2A2 cos ϕ]1/2A=[A^{2}+A^{2}+2A^{2}\,cos\, \phi]^{1/2} or A2=A2+A2+2A2 cos ϕA^{2}=A^{2}+A^{2}+2A^{2}\,cos\,\phi or cosϕ=−12cos \phi=-\frac{1}{2} or ϕ=120∘\phi=120^{\circ}