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JEE Main 202126 AugustEvening Shift
Exam
JEE Main
Year
2021
Date
26 August
Shift
Evening Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2021 · 26 August · Evening Shift · Physics · Waves and Sound

Two waves are simultaneously passing through a string and their...

Two waves are simultaneously passing through a string and their equations are : y1=A1sink(x−vt),y2=A2sink(x−vt+x0).{y}_{1} = {A}_{1}sink ( x - vt ) , {y}_{2} = {A}_{2}sink\left(x - vt + {x}_{0}\right) . Given amplitudes A1=12mm{A}_{1} = 12mm and A2=5mm{A}_{2} = 5mm, x0=3.5cm{x}_{0} = 3 . 5cm and wave number k=6.28cm−1.k = 6 . 28{cm}^{- 1} . The amplitude of resulting wave will be _____ mm.mm .

Correct answer

0

Step-by-step solution

Δϕ=kx0=2πλx0=2π×3.5(λ=2πk=1)\Deltaϕ = {kx}_{0} = \dfrac{2\pi}{\lambda}{x}_{0} = 2\pi \times 3 . 5\left(\lambda = \dfrac{2\pi}{k} = 1\right)

=2π×3510=7π= 2\pi \times \dfrac{35}{10} = 7\pi

AR=122+52+2×12×5×cos⁡(7π)=(12−5)2=7mm{A}_{R} = \sqrt{{12}^{2} + {5}^{2} + 2 \times 12 \times 5 \times \cos ( 7\pi )} = \sqrt{( 12 - 5{)}^{2}} = 7mm

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