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  1. If density of oxygen is 16 times that of hydrogen, what will be their corresponding ratio of velocity of sound?
    1. 4 : 1
    2. 2 : 1
    3. 1 : 16
    4. 1 : 4
Correct Option: D

The velocity of sound in a gas is given by

v =
γp
ρ
....(i)
Clearly, velocityv 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) and the same value of g. If r1 and r2 be their densities, then velocity of sound in the two gases are
v1 =
γp
ρ1

and v2 =
γp
ρ2

v1
=
ρ2
v2ρ1
....(ii)
For example, density of oxygen is 16 times the density of hydrogen, therefore from (ii), we have
vH
=
ρo
voρH

=
16pH
= 4
PpH

or vH = 4vo
So the corresponding ration of velocity of sound in oxygen and hydrogen is 1:4.



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