The velocity of sound in hydrogen gas at temperature 0°C is 1320m/s. Find the velocity of sound in a mixture consisting of two parts by volume of hydrogen and one part by volume of oxygen at same temperature.

Solution

Let ρ₁ be the density of hydrogen and ρ₂ be the density of oxygen at 0°C.
The molecular weight of oxygen is 16 times as that of hydrogen.
Therefore,
ρ₂= 16 ρ₁Density of the mixture consisting of two parts by volume of hydrogen and one part by volume of oxygen is.
$straight rho equals fraction numerator 2 straight rho subscript 1 plus 1 straight rho subscript 2 over denominator 3 end fraction equals fraction numerator 2 straight rho subscript 1 plus 16 straight rho subscript 1 over denominator 3 end fraction equals 6 straight rho subscript 1$
As, velocity of longitudnal wave is given by,
   $straight v equals square root of 1 over straight rho end root$
∴    $straight v subscript straight m over straight v subscript straight h equals square root of straight rho subscript 1 over straight rho end root$
$rightwards double arrow$ $straight v subscript straight m equals straight v subscript straight h square root of straight rho subscript 1 over straight rho end root equals 1320 square root of 1 over 6 end root$
   $equals 538.77 straight m divided by straight s$