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 individu

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

TestHub · Accepted Answer

When two waves of the same frequency superimpose, the resultant amplitude is given by
$A_{resultant} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos ϕ}$
$\Rightarrow \sqrt{3} A = \sqrt{A^{2} + A^{2} + 2 A^{2} \cos ϕ}$
$\Rightarrow 3 A^{2} = 2 A^{2} + 2 A^{2} \cos ϕ$
$\Rightarrow \cos ϕ = \frac{1}{2}$
$∴ ϕ = 60 °$
$∴$ Phase difference $= 60$ degree

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