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

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9\,kg$ is suspended from the wire. When this mass is replaced by a mass $M,$ the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of $M$ is .... $kg$
  • ✓
    $25$
  • B
    $5$
  • C
    $12.5$
  • D
    $1/25$
✓

Answer

Correct option: A.
$25$
a
$F = \frac{{\rm{n}}}{{2\ell }}\sqrt {{\rm{T}}/\mu } \quad $   { ${{\rm{n}} \to {{\rm{n}}^{{\rm{th}}}}}$ Harmonic or $n$ atinodes}

In case $(i)$ $\mathrm{f}=\frac{5}{2 \ell} \sqrt{\frac{90}{\mu}}$

In case $(ii)$ $\mathrm{f}=\frac{3}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mu}}$

$\Rightarrow \mathrm{T}=50 \mathrm{\,N}$ or $\mathrm{M}=5 \mathrm{\,kg}$

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