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Waves and Sound — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsWaves and Sound1 Mark
MCQ
A string of length $2 \mathrm{~m}$ is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of $500 \mathrm{~Hz}$ then the waves would travel on its with a velocity of
  • A
    $125 \mathrm{~m} / \mathrm{s}$
  • B
    $250 \mathrm{~m} / \mathrm{s}$
  • ✓
    $500 \mathrm{~m} / \mathrm{s}$
  • D
    $1000 \mathrm{~m} / \mathrm{s}$
✓

Answer

Correct option: C.
$500 \mathrm{~m} / \mathrm{s}$
(c) For string $\lambda=\frac{2 l}{p}$where $p=$ No. of loops ($=$ Order of vibration)
Hence for forth mode $p=4\Rightarrow\lambda=\frac{l}{2}$
Hence $(v=n\lambda=500\times\frac{2}{2}=500 \mathrm{~Hz})$

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