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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
Oxygen is $16$ times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is
  • ✓
    $ \sqrt {\frac{2}{{17}}} $
  • B
    $\sqrt {\frac{{32}}{{17}}} $
  • C
    $\sqrt 8 $
  • D
    $\sqrt {\frac{1}{8}} $
✓

Answer

Correct option: A.
$ \sqrt {\frac{2}{{17}}} $
a
(a) Density of mixture  $ = {\rho _{mix}} = \frac{{{V_{{O_2}}}{\rho _{{O_2}}} + {V_{{H_2}}}{\rho _{{H_2}}}}}{{{V_{{O_2}}} + {V_{{H_2}}}}}$

$ = \frac{{V\left( {{\rho _{{O_2}}} + {\rho _{{H_2}}}} \right)}}{{2\,V}} = \frac{{{\rho _{{O_2}}} + {\rho _{{H_2}}}}}{2}$              (since${V_{{O_2}}} = {V_{{H_2}}} = V$) 

$ = \frac{{{\rho _{{H_2}}} + 16{\rho _{{H_2}}}}}{2} = 8.5{\rho _{{H_2}}}$

==> $v \propto \frac{1}{{\sqrt \rho }}$

==>$\frac{{{V_{mix}}}}{{{V_{{H_2}}}}} = \sqrt {\frac{{{\rho _{{H_2}}}}}{{{\rho _{mxn}}}}}  = \sqrt {\frac{{{\rho _{{H_2}}}}}{{8.5{\rho _{{H_2}}}}}}  \approx \sqrt {\frac{2}{17}} $

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