Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason…

Given below are two statements: one is labelled as Assertion A and the other is labelled as
Reason $\mathrm{R}$
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
  1. Both $\mathrm{A}$ and $\mathrm{R}$ are true but $\mathrm{R}$ is NOT the correct explanation of $\mathrm{A}$
  2. $\mathrm{A}$ is true but $\mathrm{R}$ is false
  3. $\mathrm{A}$ is false but $\mathrm{R}$ is true
  4. Both $\mathrm{A}$ and $\mathrm{R}$ are true and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$

Solution

Speed of sound in a medium depends on inertial and elastic properties as $v=\sqrt{\frac{B}{P}}$ for gases and $v=\sqrt{\frac{Y}{P}}$ for solids. Since the elastic property of solid happens to be many folds greater than that of gases, the speed of sound in solids is higher than in gases.
Also, bulk modulus of gases varies between 0 and $\infty\left(B=-v \frac{d P}{d v}\right)$ hence reason is false.

Asked in: JEE Main 2025 (28 Jan Shift 1)

Practice more Waves and Sound questions on Aicharya