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NEET 2012
Exam
NEET
Year
2012
Subject
Physics
Chapter
Oscillations

NEET 2012 · Physics · Oscillations

The equation of a simple harmonic wave is given by y=3 (π)/(2)( 50...

The equation of a simple harmonic wave is given by y=3 \sin π2(\frac{\pi}{2}(50 t-x) where xx and yy are in metres and tt is in seconds. The ratio of maximum particle velocity to the wave velocity is

Options

  1. A2π2 \pi
  2. B32π\frac{3}{2} \pi
  3. C3π3 \pi
  4. D23π\frac{2}{3} \pi

Correct answer

B. 32π\frac{3}{2} \pi

Step-by-step solution

We know thatvmax =aωv=nλ∴vmax⁡v=aωnλ=a(2πn)nπ=2πaλ=2πa2π/k=ka=π2×3=3π2\begin{aligned}& v_{\text{max }}=a \omega\\ & v=n \lambda \\ & \therefore \quad \frac{v_{\max }}{v}=\frac{a \omega}{n \lambda}\\ & =\frac{a(2 \pi n)}{n \pi}=\frac{2 \pi a}{\lambda}\\ & =\frac{2 \pi a}{2 \pi / k}\\ & =k a=\frac{\pi}{2} \times3 \\ & =\frac{3 \pi}{2}\\ & \end{aligned}
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