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NEET 2010
Exam
NEET
Year
2010
Subject
Physics
Chapter
Waves and Sound

NEET 2010 · Physics · Waves and Sound

A transverse wave is represented by y=A (ω t-k x) . For what value...

A transverse wave is represented by y=Asin⁡(ωt−kx)y=A \sin (\omega t-k x). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

Options

  1. AπA/2\pi \mathrm{A} / 2
  2. BπA\pi \mathrm{A}
  3. C2πA2 \pi \mathrm{A}
  4. DA\mathrm{A}

Correct answer

C. 2πA2 \pi \mathrm{A}

Step-by-step solution

Wave velocity v=λT=ωλ2π\mathrm{v}=\frac{\lambda}{\mathrm{T}}=\frac{\omega \lambda}{2 \pi} Maximum particle velocity (vmax⁡)p=Aω\left(v_{\max }\right)_p=A \omega Given,v=(vmax⁡)pωλ2π=Aω⇒λ=2πA\begin{aligned}& \mathrm{v}=\left(\mathrm{v}_{\max }\right)_p \\ & \frac{\omega \lambda}{2 \pi}=A \omega\\ & \Rightarrow \quad \lambda=2 \pi \mathrm{A}\\ & \end{aligned}
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