Know that, in general, sound travels faster in solids than in liquids and faster in liquids than in gases

Cambridge IGCSE Physics 0625 – Topic 3.4 Sound

Learning Objective

Know that, in general, sound travels faster in solids than in liquids and faster in liquids than in gases.

Why Does Sound Travel at Different Speeds?

Sound is a longitudinal mechanical wave. Its speed depends on how quickly adjacent particles can transmit the disturbance. Two main material properties control this:

• Elastic property (stiffness) – how strongly the material resists deformation.
• Inertial property (density) – how much mass must be moved.

In general, solids are both stiffer and less compressible than liquids, while gases are the least stiff and most compressible. Consequently:

1. Solids have the highest stiffness‑to‑density ratio → highest sound speed.
2. Liquids have a lower stiffness‑to‑density ratio than solids → intermediate speed.
3. Gases have the lowest stiffness‑to‑density ratio → lowest speed.

Mathematical Expressions for Sound Speed

For a solid (where the relevant elastic modulus is Young’s modulus \$E\$):

\$v_{\text{solid}} = \sqrt{\frac{E}{\rho}}\$

For a fluid (liquid or gas) the bulk modulus \$K\$ is used:

\$v_{\text{fluid}} = \sqrt{\frac{K}{\rho}}\$

In an ideal gas the bulk modulus can be expressed as \$K = \gamma p\$, giving the familiar formula

\$v_{\text{gas}} = \sqrt{\frac{\gamma p}{\rho}} = \sqrt{\gamma R T}\$

where \$\gamma\$ is the ratio of specific heats, \$p\$ the pressure, \$R\$ the specific gas constant and \$T\$ the absolute temperature.

Typical Speeds of Sound in Common Media

Factors That Modify the Speed in Each State

• Solids: Type of material (different \$E\$), temperature (affects \$E\$ and \$\rho\$).
• Liquids: Temperature (affects \$K\$ and \$\rho\$), composition (e.g., salt water vs. fresh water).
• Gases: Temperature (directly increases \$v\$), molecular weight (heavier gases travel slower), humidity (water vapour reduces average molecular weight).

Example Calculation

Calculate the speed of sound in dry air at 25 °C. Use \$\gamma = 1.40\$, \$R = 287\ \text{J kg}^{-1}\text{K}^{-1}\$, and \$T = 298\ \text{K}\$.

\$v = \sqrt{\gamma R T} = \sqrt{1.40 \times 287 \times 298} \approx 346\ \text{m s}^{-1}\$

Summary

Because sound propagation requires both elasticity and inertia, the relative magnitudes of these properties in different states of matter dictate the speed:

• Solids: high stiffness → fastest.
• Liquids: moderate stiffness → intermediate.
• Gases: low stiffness → slowest.

Understanding these relationships helps explain everyday observations, such as why you hear a train whistle more clearly through the rails than through the air.