Two waves are simultaneously passing… - JEE Main 2021 Physics PYQ

JEE Main 2021 — Physics Waves & Oscillations

2021integermedium

Two waves are simultaneously passing through a string and their equations are : ${y}_{1}={A}_{1}\mathrm{sin}k(x-vt),{y}_{2}={A}_{2}\mathrm{sin}k(x-vt+{x}_{0}).$ Given amplitudes ${A}_{1}=12\mathrm{mm}$ and ${A}_{2}=5\mathrm{mm}$ , ${x}_{0}=3.5\mathrm{cm}$ and wave number $k=6.28{\mathrm{cm}}^{-1}.$ The amplitude of resulting wave will be _____ $\mathrm{mm}.$

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Held on 26 Aug 2021 · Verified 6 Jul 2026.

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Solution

$\Delta \phi ={\mathrm{kx}}_{0}=\frac{2\pi }{\lambda }{x}_{0}=2\pi \times 3.5(\lambda =\frac{2\pi }{k}=1)$

$=2\pi \times \frac{35}{10}=7\pi$

${A}_{R}=\sqrt{{12}^{2}+{5}^{2}+2\times 12\times 5\times \mathrm{cos}(7\pi )}=\sqrt{(12-5{)}^{2}}=7\mathrm{mm}$

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