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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(C) \(60\)

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\(A _{\text {resultrant }}=\sqrt{ A _{1}^{2}+ A _{2}^{2}+2 A _{1} A _{2} \cos \phi}\)

\(\sqrt{3} A =\sqrt{ A ^{2}+ A ^{2}+2 A ^{2} \cos \phi}\)

\(3 A ^{2}=2 A ^{2}+2 A ^{2} \cos \phi\)

\(\cos \phi=\frac{1}{2}\)

\(\therefore \phi=60^{\circ}\)

\(\therefore \text { Phase difference }=60 \text { degree }\)

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