JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Waves & Sound

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Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the

3

times of amplitude of individual motions. The phase difference between the two motions is ______ (degree)

Answer: 60

Solution

When two waves of equal amplitude

A

superpose, the resultant amplitude is given by:

A_{resultant} = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos ϕ

Given:

A_{resultant} = 3 A

and

A_{1} = A_{2} = A

3 A = A^{2} + A^{2} + 2 A^{2} cos ϕ

3 A^{2} = 2 A^{2} + 2 A^{2} cos ϕ

3 A^{2} = 2 A^{2} (1 + cos ϕ)

cos ϕ = \frac{1}{2}

ϕ = 6 0^{\circ}

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Integer answer

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