Question

prove that velocity of sound in hydrogen is four times that in oxygen

Answer 1

the question is very simple just remember a thing , that speed/velocity of anybody is inversely proportional to square root of molecular mass.

Hence the weight of hydrogen is less as compared to oxygen .

Here we can we proper define as :

Speed of sound is inversely proportional to the square root of molecular weight of H2 , so molecular mass of H2 is 4 , and Oxygen is 32 , so The oxygen molecular weight is 16 times greater as square root of hydrogen 4 M.W.

Answer 2

To Prove = Velocity in Hydrogen = 4 × Velocity in Oxygen

__________________________

Proof ⇒ Using the formula,

Velocity of the sound α 1/√Mass.

α shows the symbol of proportionality.

Now, In case of the Hydrogen,

Mass = 2 g.

Velocity in Hydrogen  K/√2

In Case of the Oxygen,  

Mass = 32 grams.

Velocity in Oxygen = K/√32

∴ There ratio,

Velocity in Hydrogen/Velocity in Oxygen = (K/√2)/(K/√32)

Velocity in Hydrogen/Velocity in Oxygen = √16/1

Velocity in Hydrogen/Velocity in Oxygen = 4/1

Velocity in Hydrogen = 4 × Velocity in Oxygen

Hence Proved.

Hope it helps.