Two waves executing simple harmonic motions 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). Numerical answer type. Work it out, then open the answer.

Answer: 60. Resultant amplitude AR = √(A² + A² + 2A²cos φ) = A√(2 + 2cos φ). √(2 + 2cos φ) = √(3) ⇒ 2 + 2cos φ = 3 ⇒ cos φ = 1/2. So φ = 60°.

Two waves executing simple harmonic motions travelling in the same… | JEE Main 2022 (25 Jul, Shift 2)

Q13JEE Main 2022 · 25 JUL · SHIFT 2Easy

Reflection, Superposition & Interference

Two waves executing simple harmonic motions 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).

Numerical answer type. Work it out, then open the answer.

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Answer: 60

Resultant amplitude $A_R = \sqrt{A^2 + A^2 + 2A^2\cos\phi} = A\sqrt{2 + 2\cos\phi}$ .
$\sqrt{2 + 2\cos\phi} = \sqrt{3} \Rightarrow 2 + 2\cos\phi = 3 \Rightarrow \cos\phi = \frac{1}{2}$ .
So $\phi = 60^\circ$ .

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