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STD 11 - 14. waves and sound — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. waves and sound4 Marks
MCQ
The displacement $y$ (in $cm$) produced by a simple harmonic wave is $y = \frac{{10}}{\pi }\sin \left( {2000\pi t - \frac{{\pi x}}{{17}}} \right)$. The periodic time and maximum velocity of the particles in the medium will respectively be
  • A
    ${10^{ - 3}}\,sec$ and $330 \,m/sec$
  • B
    ${10^{ - 4}}\,sec$ and $20 \,m/sec$
  • ✓
    ${10^{ - 3}}\,sec$ and $200\, m/sec$
  • D
    ${10^{ - 2}}\,sec$ and $2000\, m/sec$
✓

Answer

Correct option: C.
${10^{ - 3}}\,sec$ and $200\, m/sec$
c
(c) Comparing with $y = a\sin (\omega t - kx)$==>$a = \frac{{10}}{\pi },\omega = 2000\,\pi $

$\therefore $ ${v_{\max }} = a\omega = \frac{{10}}{\pi } \times 2000\,\pi = 200m/\sec $ 

and $\omega = \frac{{2\pi }}{T} \Rightarrow 2000\,\pi = \frac{{2\pi }}{T}$==> $T = {10^{ - 3}}\,sec$

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