Class 11 > Unit # 12:Acoustics > Factors affecting Speed of Sound in Air

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Factors Affecting the Speed of Sound in Air

Video Lecture: Factors Affecting Speed of Sound

Watch the complete step-by-step video lecture explaining how density, moisture, pressure, temperature, and wind affect the speed of sound in air:

Factors Affecting the Speed of Sound in Air

Since sound waves are compressible mechanical waves, the nature and physical state of the medium significantly influence their propagation. The primary factors affecting the speed of sound in air include density, moisture, pressure, temperature, and wind velocity.

1. Density of Air

From Laplace's corrected formula for the speed of sound in a gas:

$v = \sqrt{\frac{\gamma P}{\rho}}$

At constant pressure, the speed of sound varies inversely with the square root of the density of air ($\rho$):

$v \propto \frac{1}{\sqrt{\rho}}$

Thus, sound travels faster in gases of lower density than in denser gases.

2. Moisture (Humidity)

Moisture refers to the presence of water vapor suspended in the air. Water vapor ($H_2O$, molar mass $\approx 18\text{ g/mol}$) is less dense than dry air (average molar mass $\approx 29\text{ g/mol}$). Consequently, the presence of moisture decreases the net density of humid air compared to dry air. Because speed is inversely proportional to the square root of density, the speed of sound in damp (humid) air is greater than in dry air.

3. Pressure

According to the Ideal Gas Law for $n$ moles:

$PV = nRT \implies P = \frac{nRT}{V} = \frac{m}{M \cdot V}RT = \rho RT$

Where $\rho = \frac{m}{V}$ represents the density of the gas. Substituting this density expression into the speed formula:

$v = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{\gamma P}{\frac{P}{RT}}} = \sqrt{\frac{\gamma RT}{M}}$

Conclusion on Pressure: The pressure term $P$ cancels out from the equation. This proves that the speed of sound is independent of changes in the pressure of a gas at constant temperature.

4. Temperature

Temperature changes do not significantly alter the speed of sound in liquids and solids, but they have a profound effect on gases. From the velocity relation $v = \sqrt{\frac{\gamma RT}{M}}$, the speed of sound is directly proportional to the square root of absolute temperature ($T$ in Kelvin):

$v \propto \sqrt{T}$

For temperatures near $0^\circ\text{C}$, the speed of sound increases by approximately $0.6\text{ m/s}$ for each $1^\circ\text{C}$ rise in temperature. The corrected velocity equation at temperature $t^\circ\text{C}$ is expressed as:

$v_t = v_0 + 0.6t$

Where $v_0$ is the speed of sound at $0^\circ\text{C}$ ($273\text{ K}$) and $v_t$ is the speed at temperature $t^\circ\text{C}$.

5. Wind Velocity

If air is in motion with wind speed $w$, the net speed of sound relative to the ground is affected by the direction of the wind:

• When moving along the direction of the wind: $v_{\text{net}} = v + w$
• When moving against the direction of the wind: $v_{\text{net}} = v - w$

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