Speed increases as temperature increases.
Explanation
Sound waves are mechanical waves that propagate through a medium via the vibration of particles. In gases, the speed of sound is governed by the physical properties of the medium, specifically its temperature, density, and adiabatic index.
Detailed Analysis:
The speed of sound ($v$) in an ideal gas is mathematically represented by the formula derived from the Laplace correction to Newton's formula:
$v = \sqrt{\frac{\gamma RT}{M}}$
Where:
- $\gamma$ is the adiabatic index (ratio of specific heats).
- $R$ is the universal gas constant.
- $T$ is the absolute temperature of the gas.
- $M$ is the molar mass of the gas.
From this equation, it is evident that the speed of sound is directly proportional to the square root of the absolute temperature ($v \propto \sqrt{T}$). As the temperature of the gas increases, the kinetic energy of the gas molecules increases, allowing the pressure disturbance (sound wave) to be transmitted more rapidly through the medium. Therefore, the speed of sound increases as the temperature rises.
Key Takeaway:
The speed of sound in a gas is directly proportional to the square root of its absolute temperature. For air, the speed increases by approximately 0.61 m/s for every 1°C rise in temperature.