If Cs be the velocity of sound in air and C be the r.m.s velocity, then

Question

If Cs be the velocity of sound in air and C be the r.m.s velocity, then (A) Cs < C (B) Cs = C (C) Cs = C(&gamma;/3)1/2 (D) None of these

Tardigrade Admin · Accepted Answer

Velocity of sound (Cs) = √(&gamma; P/ρ) R.M.S. velocity of gas molecules =√(3P/ρ) (CS/C) = √(&gamma; P/ρ )× (ρ/3P) = √(&gamma;/3) ⇒ Cs =C ×√(&gamma;/3)

Q. If $C_{s}$ be the velocity of sound in air and C be the r.m.s velocity, then

$C_{s} < C$

$C_{s} = C$

$C_{s} = C (γ /3)^{1/2}$

None of these

Velocity of sound $(C_{s}) = \frac{γ P}{ρ}$
R.M.S. velocity of gas molecules $= \frac{3 P}{ρ}$
$\frac{C _{S}}{C} = \frac{γ P}{ρ} \times \frac{ρ}{3 P} = \frac{γ}{3} \Rightarrow C_{s} = C \times \frac{γ}{3}$

Q. If Cs​ be the velocity of sound in air and C be the r.m.s velocity, then

Cs​<C

Cs​=C

Cs​=C(γ/3)1/2