Question

Assertion (A): Sound travels slower in gases than in solids.
Reason (R): Gases have a lower density than solids.
In light of the above statements , choose the correct answer from the option given below.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.
• E. Both (A) and (R) are false.

Hint:

In speed of sound problems, elasticity is usually the "stronger" factor compared to density when comparing different states of matter.

Answer 1

The Correct Option is B

Concept: The speed of sound $v$ in a medium is given by: \[ v = \sqrt{\frac{E}{\rho}} \] where $E$ is the elasticity (Bulk modulus or Young's modulus) and $\rho$ is the density.
Step 1: Evaluate Assertion (A).
Sound travels fastest in solids and slowest in gases because solids are much more elastic (stiff) than gases. Thus, (A) is true.

Step 2: Evaluate Reason (R).
It is a physical fact that gases generally have lower density than solids. Thus, (R) is true.

Step 3: Evaluate the relationship.
While density affects speed, the primary reason sound is faster in solids is their significantly higher elasticity, which outweighs the higher density. Therefore, (R) is not the correct explanation for (A).