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JEE Main 2022 (29 Jun, Shift 1) · Progressive Wave Equation

Progressive Wave Equation question from JEE Main 2022 (29 Jun, Shift 1)

Q65JEE Main 2022 · 29 JUN · SHIFT 1Medium

Progressive Wave Equation

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

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Answer: (b)

  1. Wave velocity v=nλv = n\lambda; maximum particle velocity =2πn(10) cm/s= 2\pi n (10)\text{ cm/s}
  2. 20πn=4nλ⇒λ=5π cm20\pi n = 4 n\lambda \Rightarrow \lambda = 5\pi\text{ cm}
  3. So the answer is (b) 5π5\pi.
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