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
Diffcult
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(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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