Steel vs Air Sound Speed Assertion

This section examines the claim that sound waves travel faster in steel compared to air at the same temperature.

Sound travels as vibrations through a medium. The speed at which these vibrations travel depends heavily on the properties of the medium itself.

Specifically, the speed of sound is influenced by how closely packed the particles are and the strength of the forces between them (intermolecular forces). It is generally understood that sound travels faster in denser and stiffer materials.

• Steel is a solid material. Its particles are packed very closely together, and the forces between these particles are strong.
• Air is a gas. Its particles are much farther apart, and the forces between them are very weak.

Because of these differences, vibrations can be passed from one particle to the next much more quickly in steel than in air. Typical speeds confirm this:

• Speed of sound in steel is approximately 5960 meters per second (m/s).
• Speed of sound in air (at 20°C) is approximately 343 meters per second (m/s).

Therefore, Assertion (A) is true.

Sound Speed Reason Analysis

This part evaluates the reason provided for the difference in sound speeds: the closer packing and stronger intermolecular forces in solids like steel compared to gases like air.

The transmission of sound relies on the collision or interaction between adjacent particles in the medium. When one particle vibrates, it causes its neighbor to vibrate.

• In materials like steel, the particles are very close, allowing vibrations to be transferred rapidly from one particle to the next. The strong intermolecular forces also help in efficiently propagating these vibrations.
• In materials like air, the particles are far apart. A vibrating particle needs to travel a greater distance before colliding with another particle, slowing down the overall transmission of the vibration. The weak intermolecular forces contribute to this slower transfer.

The relationship can be conceptually understood through factors like elasticity and density. While steel is denser than air, its elasticity (stiffness) is vastly higher. The speed of sound ($v$) is generally related to the medium's elasticity (e.g., Bulk Modulus, $B$) and density ($\rho$) by an expression similar to $v = \sqrt{\frac{B}{\rho}}$. The significantly higher elasticity of steel makes sound travel much faster.

Thus, the reason correctly explains why sound travels faster in steel than in air. Reason (R) is true and is the correct explanation of Assertion (A).

Assertion and Reason Validity Conclusion

Based on the analysis, both the assertion and the reason are factually correct. Furthermore, the reason accurately identifies the physical properties of the media (steel and air) that cause the difference in sound wave speed.