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

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
Standing waves are generated on a sonometer string loaded with a cylindrical body. If the cylinder is completely immersed in water, the length of the loops changes by a factor of $2.2$ . The specific gravity of the material of the cylinder is 
  • A
    $1.11$
  • B
    $2.15$
  • C
    $2.50$
  • ✓
    $1.26$
✓

Answer

Correct option: D.
$1.26$
d
$f=\frac{V}{\lambda_{1}}=\frac{1}{\lambda_{1}} \sqrt{\frac{T_{1}}{\mu}}$

$\mathrm{f}=\frac{\mathrm{V}}{\lambda_{1}}=\frac{1}{\lambda_{1}} \sqrt{\frac{\mathrm{T}_{2}}{\mu}}$

$\frac{1}{\lambda_{1}} \sqrt{\frac{T_{1}}{\mu}}=\frac{1}{\lambda_{2}} \sqrt{\frac{T_{2}}{\mu}}$

$\sqrt{\frac{\mathrm{T}_{1}}{\mu}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right) \sqrt{\frac{\mathrm{T}_{2}}{\mu}}$

$\mathrm{T}_{1}=(2.2)^{2} \cdot \mathrm{T}_{2}$

$\mathrm{Mg}=4.84\left[\mathrm{Mg}-\frac{\mathrm{M}}{(\mathrm{S} \cdot \mathrm{G})} \cdot \mathrm{g}\right]$

$1=4.84-\frac{4.84}{\mathrm{S.G}}$

$\frac{4.84}{\mathrm{S.G}}=3.84 \Rightarrow \mathrm{S.G}=\frac{4.84}{3.84}$

$\Rightarrow \mathrm{S.G}=1.26$

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