The displacements of two particles executing simple harmonic motion are represented as y 1 = 2 sin ( 10 t + θ ) and y 2 = 3 cos 10 t . The phase difference between the velocities of these waves is

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The displacements of two particles executing simple harmonic motion are represented as y 1 ​ = 2 sin ( 10 t + θ ) and y 2 ​ = 3 cos 10 t . The phase difference between the velocities of these waves is

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y 1 ​ y 2 ​ ​ = 2 sin ( 10 t + θ ) ∴ V 1 ​ = dt dy 1 ​ ​ = 20 cos ( 10 t + θ ) = 3 cos 10 t = − 30 cos ( 2 π ​ − 10 t ) = − 30 cos ( 10 t − 2 π ​ ) = 30 cos ( 10 t − 2 π ​ + π ) = 30 cos ( 10 t + 2 π ​ ) ​ ∴ phase difference between V 1 ​ and V 2 ​ = ( 10 t + θ ) − ( 10 t + 2 π ​ ) = ( θ − 2 π ​ )

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