# If density of oxygen is 16 times that of hydrogen, what will be their corresponding ratio of velocity of sound -

 [ A ]    1: 4 [ B ]    1: 16 [ C ]    2: 1 [ D ]    4: 1
 Answer : Option A Explanation : The velocity of sound in a gas is given by v = g r p.... (i) Clearly, velocity v is inversely proportional to the square root of density (r) of the gas.Now, let us consider two gases which are at the same pressure (P) & the same value of g. If r1 & r2 be their densities, then velocity of sound in the two gases are v1 = g r p 1 & v2 = g r p 2 \ v v 1 2 2 1 = r r.... (ii) For example, density of oxygen is 16 times the density of hydrogen, so from (ii), we have v v pH PpH H o H = = = r r 0 16 4 or v v H = 4 0 So the corresponding ration of velocity of sound in oxygen & hydrogen is 1:4.