Question

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)

Answer 1

$ A _{\text {resultant }}=\sqrt{ A _1^2+ A _2^2+2 A _1 A _2 \cos \phi} $
$\Rightarrow \sqrt{3} A =\sqrt{ A ^2+ A ^2+2 A ^2 \cos \phi} $
$ \Rightarrow 3 A ^2=2 A ^2+2 A ^2 \cos \phi$
$ \Rightarrow \cos \phi=\frac{1}{2}$
$ \therefore \phi=60^{\circ} $
$ \therefore $ Phase difference $=60 $ degree