JEE Main 2023 · 6 April · evening · Single correct · +4 / −1

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

  1. (a) 1: 1
  2. (b) 1: 2
  3. (c) 1: 4
  4. (d) 4: 1
Answer and solution

Answer (d) 4: 1

Solution

Physics sir · 4 steps

Both gases are diatomic, so γ cancels and only the molar masses decide the ratio.

  1. Laplace formula. The speed of sound in a gas depends on γ, the temperature T and the molar mass M.

    v = √((γ R T)/M)

  2. Cancel common factors. H₂ and O₂ are both diatomic, so both have γ = 1.4. The temperature is the same too. That leaves v ∝ 1/√M.
  3. Put in masses. v_(H₂)/v_(O₂) = √(M_(O₂)/M_(H₂)) = √(32/2) = √16 = 4.
  4. So. Sound travels 4 times faster in hydrogen than in oxygen, so the ratio is 4 : 1, option (d).

The idea to keep. For gases with the same γ at the same temperature, v ∝ 1/√M. The lighter gas carries sound faster, so always check that the lighter gas ends up with the bigger number.

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

Study Sound Waves

Asked about 40 times in JEE Main since 2020. This question is from 2023.