Question

when two displacements represented by y1 = a sin (ωt) and y2 = b cos (ωt) are super- imposed the motion is:

Answer 1

Explanation:

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Answer 2

amplitude of new wave is √(a² + b²) and phase difference of the wave is tan-¹(b/a)

Two displacements represented by y1 = a sinωt and y2 = b cosωt are superimposed.

so new wave after superimposition, y = y1 + y2

= asinωt + bcosωt

= √(a² + b²) [a/√(a² + b²) sinωt + b/√(a² + b²) cosωt]

let cosα = a/√(a² + b²) then sinα = b/√(a² + b²)

= √(a² + b²)[cosα.sinωt + sinα.cosωt ]

using formula, sin(A + B) = sinA.cosB + sinB.cosA

= √(a² + b²) sin(ωt + α)

hence, amplitude of new wave is √(a² + b²)

phase difference, α = tan-¹(b/a)

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