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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
The speed of sound in hydrogen at $NTP$ is $1270\,m/s$ . Then, the speed in a mixture of hydrogen and oxygen in the ratio $4 : 1$ by volume will be ..... $m/s$
  • A
    $317$
  • ✓
    $635$
  • C
    $830$
  • D
    $950$
✓

Answer

Correct option: B.
$635$
b
Suppose $V$ be the volume of oxygen. The volume of hydrogen will be $4 \mathrm{V}$. If $\rho_{\mathrm{m}}$ be the density of the mixture, then

$\rho_{\mathrm{m}}=\frac{4 \mathrm{V} \times 1+\mathrm{V} \times 16}{5 \mathrm{V}}=4$

i.e., density of mixture is 4 times that of hydrogen. $\mathrm{As}$

$\mathrm{V} \propto(1 / \rho)^{1 / 2}$

Velocity in mixture $=\frac{1270}{(4)^{1 / 2}}=635 \mathrm{\,m} / \mathrm{s}$

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