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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
The frequency of a sonometer wire is $100 Hz$. When the weights producing the tensions are completely immersed in water, the frequency becomes $80 Hz$ and on immersing the weights in a certain liquid, the frequency becomes $60 Hz$. The specific gravity of the liquid is 
  • A
    $1.42$
  • ✓
    $1.77$
  • C
    $1.82$
  • D
    $1.21$
✓

Answer

Correct option: B.
$1.77$
b
(b)

As we know, frequency

$f \propto \sqrt{m g}$ or $f \propto \sqrt{g}$

In water, $f _{ w }=0.8 f _{ air }$

$\frac{ g ^{\prime}}{ g }(0.8)^2=0.64$

$\Rightarrow 1-\frac{\rho_{ w }}{\rho_{ m }}=0.64$

$\Rightarrow \frac{\rho_{ W }}{\rho_{ m }}=0.36$

In liquid, $\frac{ g ^{\prime}}{ g }=(0.6)^2=0.36$

$1-\frac{\rho_1}{\rho_{ m }}=0.36 \frac{\rho_1}{\rho_{ m }}=0.64$

From eq. $(1)$ and $(2)$

$\frac{\rho_l}{\rho_n}=\frac{0.64}{0.36} \quad \therefore \quad \rho_l=1.77$

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