JEE Main 2023PhysicsWaves and SoundEasyNumerical

JEE Main 2023 — Waves and Sound Question with Solution

JEE Main 2023 (31 Jan Shift 2)

Question

The displacement equations of two interfering waves are given by y1=10 sin ωt+π3 cm, y2=5sin ωt+3 cos ωt cm respectively. The amplitude of the resultant wave is _____ cm.

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Show full solutionCorrect answer: 20
Correct answer
20

Step-by-step explanation

Displacement equation of second wave can be written as,y2=5sinωt+3cosωt=10sinωt×12+32×cosωt=10sinωt×cosπ3+sinπ3×cosωt

=10sinωt+π3

As we can see, the phase difference between the waves is 0. Therefore, resultant amplitude will be sum of the amplitudes of the waves.

So A=A1+A2=10 cm+10 cm=20 cm

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About this question

This is a previous-year question from JEE Main 2023, covering the Waves and Sound chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.