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

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
A standing wave exists in a string of length $150\ cm$ , which is fixed at both ends with rigid supports . The displacement amplitude of a point at a distance of $10\ cm$ from one of the ends is $5\sqrt 3\ mm$ . The nearest distance between the two points, within the same loop and havin displacment amplitude equal to $5\sqrt 3\  mm$ is $10\ cm$ . Find the maximum displacement amplitude of the particles in the string .... $mm$
  • A
    $20$
  • B
    $15$
  • ✓
    $10$
  • D
    None of these
✓

Answer

Correct option: C.
$10$
c
$y = \Lambda \sin kx\,\cos \omega t$

$5 \sqrt{3}=\mathrm{A\,sin\,k} \times 10$

$5 \sqrt{3}=\mathrm{A} \sin \mathrm{k} \times 20$

After solving $\mathrm{k}=\frac{\pi}{30}$

$5\sqrt 3  = {\mathop{\rm Asin}\nolimits} \left( {\frac{{II}}{{30}} \times 10} \right) \to {\rm{A}} = 10\,{\rm{mm}}$

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