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Q.

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 $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is ______ (degree)

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answer is 60.

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Detailed Solution

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$\begin{array}{l} A_{resultant} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos ϕ} \\ \Rightarrow \sqrt{3} A = \sqrt{A^{2} + A^{2} + 2 A^{2} \cos ϕ} \\ \Rightarrow 3 A^{2} = 2 A^{2} + 2 A^{2} \cos ϕ \\ \Rightarrow \cos ϕ = \frac{1}{2} \\ ∴ ϕ = 60^{\circ} \\ ∴ Phase difference = 60 degree \end{array}$

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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)