Question

if pressure of a gas at aconstant temperature is incceased 4 times how the volicity of sound in the gas will be affected?

Answer 1

Let velocity be v₁ at the sound pressure be P₁

velocity be v₂ at the sound pressure be P₂

P₂ = 4P₁

m/V₁ = ρ₁

=> v₁ = √(γP₁/ρ₁ )

=> v₁ = √(γP₁V₁ /m )---1

Now when pressure becomes P₂ let density become ρ₂ = m/V₂

Thus,

v₂ = √(γP₂V₂ /m ) ---2

Now by Boyle’s law

P₁V₁ = P₂V₂ ---3.

By eqn. 2 and 3

v₂ = √(γ P₁V₁/m )

=> v₂ = v₁

Thus velocity of sound does not change with increase in pressure.