How does the velocity of sound waves in air vary with temperature, assuming normal atmospheric conditions?

Introduction / Context:
The speed of sound in gases is a fundamental acoustic property that influences microphone calibration, room acoustics, sonar, and atmospheric acoustics. Temperature dependence is particularly important for precise measurement and system design.

Given Data / Assumptions:

• Ideal-gas approximation for air.
• Neglect humidity and wind for the basic relation.

Concept / Approach:

For an ideal gas, speed of sound c = sqrt(γ * R * T / M), where γ is ratio of specific heats, R is the universal gas constant, M is molar mass, and T is absolute temperature. Thus, c ∝ sqrt(T).

Step-by-Step Solution:

Verification / Alternative check:

Empirical formula: c ≈ 331 m/s + 0.6 m/s per °C at moderate temperatures; this approximates the sqrt(T) dependence around standard conditions.

Why Other Options Are Wrong:

• Constant: contradicts both theory and measurement.
• Directly proportional to T or inversely proportional to T: incorrect functional dependence.
• Independent of humidity/temperature: humidity has a small effect; temperature a major one.

Common Pitfalls:

Assuming a linear dependence across all temperatures; the linear relation is only a local approximation.

Final Answer:

Directly proportional to the square root of absolute temperature