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JEE Main 202229 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
29 June
Shift
Morning Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2022 · 29 June · Morning Shift · Physics · Waves and Sound

A longitudinal wave is represented by y = 10 2π(nt - (x)/(λ))cm ....

A longitudinal wave is represented by y=10sin⁡2π(nt−xλ)cmy = 10\sin 2\pi\left(nt - \dfrac{x}{\lambda}\right)cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to

Options

  1. A2π2\pi
  2. B5π5\pi
  3. Cπ\pi
  4. D5π2\dfrac{5\pi}{2}

Correct answer

B. 5π5\pi

Step-by-step solution

As we know particle velocity, vp=dydt=(10×2\pin)×cos⁡2π(nt−xλ){v}_{p} = \dfrac{dy}{dt} = \left(10 \times 2\pin\right) \times \cos 2\pi\left(nt - \dfrac{x}{\lambda}\right)

Therefore, {\left({v}_{p}\right)}_\max = 20\pin

Now as we know, v=\lambdanv = \lambdan

As given in the question,

{\left({v}_{p}\right)}_\max = 4v ⇒ 20\pin = 4\lambdan ⇒ \lambda = 5\pi

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