The speed of sound in oxygen at S.T.P. will be approximately: (given, R=8.3 JK⁻¹, γ=1.4)

Solution

Physics sir · 4 steps

Use Laplace's formula with oxygen's molar mass in kilograms, and keep T at 273 K for STP.

1. Laplace formula. Sound compresses a gas adiabatically, so its speed depends on γ, the gas constant, the temperature and the molar mass M.

   v = √((γ R T)/M)

2. Values for oxygen. STP means T = 273 K. For O₂, M = 32 g mol⁻¹ = 0.032 kg mol⁻¹, and γ = 1.4.
3. Put in numbers. γ R T = 1.4 × 8.3 × 273 = 3172.26. Dividing by 0.032 gives 99133 m² s⁻², and √99133 ≈ 314.9 m s⁻¹.
4. So. The speed of sound in oxygen at STP is about 315 m s⁻¹, which is option (d).

The idea to keep. For sound in any gas, use v = √(γ RT/M) with M in kg per mole. A heavier gas gives a slower speed, so oxygen comes out a little slower than air.

Answer from the NTA final answer key. Solution by PrepWiser.