Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids.
In the light of the above statements, choose the correct answer from the options given below

Solution

Physics sir · 4 steps

Speed of sound is the square root of elasticity over density, and solids win hugely on elasticity.

1. What sets the speed. A sound wave travels faster when the medium is harder to compress and slower when the medium is heavier. Both effects appear in one formula.

   v = √(E/ρ)

2. Check Reason R. Here E is the elastic modulus of the medium. A gas is very easy to squeeze, so its bulk modulus is tiny, about 10⁵ Pa for air. A solid like steel has a modulus near 10¹¹ Pa. So R has it backwards, and R is false.
3. Check Assertion A. Steel is about 6500 times denser than air, but its modulus is about a million times larger, so E/ρ is much bigger for the solid. That is why sound moves at about 5000 m s⁻¹ in steel and only about 340 m s⁻¹ in air. A is true.
4. So. A is true and R is false, which is option (c).

The idea to keep. For any medium, compare E/ρ. Solids are denser, but their moduli are larger by a far bigger factor, so sound is fastest in solids, then liquids, then gases.

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