QJEEM22Phe8a9: JEE Main 2022 Physics - Class 11 JEEM22Phe8a9 Solution: The equations of two waves are given by : y 1 = 5 sin 2 π (x -…

Question

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The equations of two waves are given by :

y₁ = 5 sin 2 $π$ (x - vt) cm

y₂ = 3 sin 2 $π$ (x $-$ vt + 1.5) cm

These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

Accepted Answer

$y_{1} = 5 \sin (2 π x - 2 π v t)$

$y_{2} = 3 \sin (2 π x - 2 π v t + 3 π)$

$\Rightarrow$ Phase difference = 3 $π$

$\Rightarrow A_{n e t} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos (3 π)}$

$\Rightarrow A_{n e t} = 2$ cm

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