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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
The equation of a transverse wave travelling on a rope is given by $y = 10\sin \pi (0.01x - 2.00t)$ where $y$ and $x$ are in $cm$ and $t$ in $seconds$. The maximum transverse speed of a particle in the rope is about .... $cm/s$
  • ✓
    $63$
  • B
    $75$
  • C
    $100$
  • D
    $121$
✓

Answer

Correct option: A.
$63$
a
(a) The given equation is $y = 10\sin (0.01\pi x - 2\pi t)$

Hence $\omega = $coefficient of $t = 2 \pi$

==> Maximum speed of the particle ${v_{\max }} = a\omega = 10 \times 2\pi $

$= 10 × 2 × 3.14 = 62.8 ≈ 63 cm/s$

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