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JEE Main 20179 AprilOnline
Exam
JEE Main
Year
2017
Date
9 April
Mode
Online
Subject
Physics
Chapter
Waves and Sound

JEE Main 2017 · 9 April · Online · Physics · Waves and Sound

A standing wave is formed by the superposition of two waves...

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, y(x,t)=0.5sin⁡(5π4x)cos⁡(200\pit)y\left(x, t\right) = 0.5\sin \left(\dfrac{5\pi}{4}x\right)\cos \left(200\pit\right). What is the speed of the travelling wave moving in the positive xx direction? (xx and ttare in meter and second, respectively)

Options

  1. A120ms−1120m{s}^{- 1}
  2. B90ms−190m{s}^{- 1}
  3. C160ms−1160m{s}^{- 1}
  4. D180ms−1180m{s}^{- 1}

Correct answer

C. 160ms−1160m{s}^{- 1}

Step-by-step solution

y=2asin(kx)cos⁡(\omegat)y = 2asin\left(kx\right)\cos \left(\omegat\right)

⇒k=5π4m−1,ω=200πrads−1⇒ k = \dfrac{5\pi}{4}{m}^{- 1}, \omega = 200\pi rad{s}^{- 1},

v=ωkv = \dfrac{\omega}{k}=200π5π4=160ms−1= \dfrac{200\pi}{\dfrac{5\pi}{4}} = 160m{s}^{- 1}
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