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## Homework Statement

While analyzing superposition of waves from two coherent sources ,the displacement from the two sources are written as y

_{1}=A

_{1}cos(kx-ωt) and y

_{2}=A

_{2}cos(kx-ωt+∅) .The resultant displacement at any point is given by y=y

_{1}+y

_{2}.

I am having doubt that why does argument of sine in both y

_{1}and y

_{2}contain the same variable ‘x’ . Since ‘x’ represents the distance of the point from the originating source which may be different in the two waves,the displacements should be written as y

_{1}=A

_{1}cos(kx

_{1}-ωt) and y

_{2}=A

_{2}cos(kx

_{2}-ωt+∅) .But this is not the case .

I am pretty sure I am missing something very obvious .I would be grateful if somebody could help me understand this.

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