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JEE Main 202324 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
24 January
Shift
Morning Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2023 · 24 January · Morning Shift · Physics · Waves and Sound

A travelling wave is described by the equation y(x, t) = [0 . 05...

A travelling wave is described by the equation y(x,t)=[0.05sin⁡(8x−4t)]my\left(x, t\right) = \left[0 . 05\sin \left(8x - 4t\right)\right]m. The velocity of the wave is:

[All the quantities are in SI unit]

Options

  1. A4ms−14m{s}^{- 1}
  2. B2ms−12m{s}^{- 1}
  3. C0.5ms−10 . 5m{s}^{- 1}
  4. D8ms−18m{s}^{- 1}

Correct answer

C. 0.5ms−10 . 5m{s}^{- 1}

Step-by-step solution

The given wave equation is of the form:

y=Asin(kx−\omegat)y = Asin\left(kx - \omegat\right)

with k=8k = 8 and ω=4\omega = 4

Since, k=2πλk = \dfrac{2\pi}{\lambda} and ω=2πf\omega = 2\pi f

Then, ωk=fλ=v\dfrac{\omega}{k} = f\lambda = v

⇒v=48=0.5ms−1⇒ v = \dfrac{4}{8} = 0 . 5m{s}^{- 1}

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