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

Step-by-step solution

Velocity of sound in a gas is given by v= R T M where, = specific heat ratio and M= molecular mass of gas. Fror hydrogen, v_ H = R T M₁ For mixture of gases, molecular mass, Here, M_ mix = n₁ M₁+n₂ M₂ n₁+n₂ n₁=n₂ (for equal volumes) and M₂=16 M₁ (given) M_ mix = M₁+16 M₁ 2 = 17 M₁ 2 Velocity of sound, v_ mix = R T M_ mix Dividing Eq. (ii) by Eq. (i) we get aligned v_ mix v_ H &= R T M_ mix M₁ R T &= M₁ M_ mix = 2 17 aligned