JEE MAIN - Physics (2025 - 28th January Morning Shift - No. 2)

Given below are two statements: one is labelled as $\mathbf{A s s e r t i o n} \mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

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

Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$

$\mathbf{A}$ is false but $\mathbf{R}$ is true

$\mathbf{A}$ is true but $\mathbf{R}$ is false

Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$

We know, speed of sound in a medium $$v = \sqrt {{B \over \rho }} $$ where B = bulk modulus, $\rho$ = density of the medium

Since, solids and liquids are much more difficult to compress than gases so they have much higher values of bulk modulus.

i.e., $${B_{solid}} > {B_{liquid}} > {B_{gas}}$$

Generally solids and liquids have higher mass densities ($\rho$) than gases. But corresponding increase in bulk modulus is much higher.

So, $${v_{solid}} > {v_{liquid}} > {v_{gas}}$$

Hence, option 3 is correct.