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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 travelling wave is $y=a \sin 2 \pi\left(p t-\frac{x}{5}\right)$. Then the ratio of maximum particle velocity to wave velocity is ...........
  • A
    $\frac{\pi a}{5}$
  • B
    $2 \sqrt{5 \pi a}$
  • ✓
    $\frac{2 \pi a}{5}$
  • D
    $\frac{2 \pi a}{\sqrt{5}}$
✓

Answer

Correct option: C.
$\frac{2 \pi a}{5}$
c
(c)

Equation of travelling wave

$y=a \sin 2 \pi\left(p t-\frac{x}{5}\right)$

Maximum particle velocity $\left(v_y\right)=A \omega$ or $v_y=a \times 2 \pi p$

Wave velocity $(v)=\frac{\omega}{k}=\frac{2 \pi p}{2 \pi / 5}=5 p$

$\therefore \frac{v_y}{v}=\frac{2 \pi a}{5}$

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