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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
A wire having a linear mass density $9.0 \times 10^{-4} \;{kg} / {m}$ is stretched between two rigid supports with a tension of $900\; {N}$. The wire resonates at a frequency of $500\;{Hz}$. The next higher frequency at which the same wire resonates is $550\; {Hz}$. The length of the wire is $...... {m}$
  • A
    $50$
  • B
    $100$
  • ✓
    $10$
  • D
    $2$
✓

Answer

Correct option: C.
$10$
c
$\mu=9.0 \times 10^{-4}\, \frac{{kg}}{{m}}$

${T}=900\, {N}$

${V}=\sqrt{\frac{{T}}{\mu}}=\sqrt{\frac{900}{9 \times 10^{-4}}}=1000 \,{m} / {s}$

${f}_{1}=500 \,{Hz}$

${f}=550$

$\frac{{nV}}{2 \ell}=500 \ldots . \text { (i) }$

$\frac{({n}+1) {V}}{2 \ell}=500 \ldots(ii)$

$(ii)\, (i)$ $\frac{{V}}{2 \ell}=50$

$\ell=\frac{1000}{2 \times 50}=10$

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