Two waves executing simple harmonic motion… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Waves & Oscillations

2022integereasy

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)

Official previous-year question

Held on 25 Jul 2022 · Verified 6 Jul 2026.

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Solution

When two waves of the same frequency superimpose, the resultant amplitude is given by

${A}_{\mathrm{resultant}}=\sqrt{{A}_{1}^{2}+{A}_{2}^{2}+2{A}_{1}{A}_{2}\mathrm{cos}\phi }$

$\Rightarrow \sqrt{3}A=\sqrt{{A}^{2}+{A}^{2}+2{A}^{2}\mathrm{cos}\phi }$

$\Rightarrow 3{A}^{2}=2{A}^{2}+2{A}^{2}\mathrm{cos}\phi$

$\Rightarrow \mathrm{cos}\phi =\frac{1}{2}$

$\therefore \phi =60^{\circ}$

$\therefore$ Phase difference $=60$ degree

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