What Determines the Speed of Sound in a Medium?

The speed of sound is not determined by the properties of the sound wave itself (like its frequency or amplitude). Instead, it depends entirely on the physical properties of the medium it is traveling through.

The two main factors are:

1. Elasticity (or Stiffness) of the Medium
2. Density (or Inertia) of the Medium

Speed of Sound ≈ √(Elasticity / Density)

1. Elasticity (Stiffness)

This is the dominant factor. Elasticity refers to a material's ability to resist deformation and return to its original shape after a force (like a vibration) is applied.

• High Elasticity (Stiff): Particles are strongly bonded and snap back into position very quickly. This allows them to transfer energy rapidly to their neighbors. Higher elasticity = Faster sound.
• Low Elasticity (Compressible): Particles are weakly bonded and do not return to position quickly. This results in a slower energy transfer.

This is why sound travels fastest in solids. Steel is much, much stiffer (more elastic) than air, allowing it to transmit vibrations at high speed.

2. Density (Inertia)

Density refers to the mass of a substance per unit volume. This property relates to the medium's inertia, or its resistance to being moved.

• Low Density: Particles are lightweight and easily moved by a vibration, allowing the wave to propagate quickly.
• High Density: Particles are "heavier" and have more inertia. It takes more energy to get them to move, which slows down the transfer of the sound wave. Higher density = Slower sound.

The "Contradiction" Explained: Solids vs. Gases

You might ask: "How does sound travel faster in steel than in air? Steel is much denser!"

The answer lies in the formula. While steel is thousands of times denser than air (which slows sound down), its elasticity (stiffness) is millions of times greater than air. The massive increase in stiffness far outweighs the increase in density, resulting in a much faster speed of sound.

A Special Case: Speed of Sound in Gas (Air)

For a gas like air, the main factor determining the speed of sound is temperature. (Density and pressure are related and their effects mostly cancel out).

• Hotter Gas: Molecules are moving faster and have more energy. They collide more frequently and forcefully, allowing them to transmit a sound wave more quickly.
• Cooler Gas: Molecules are slower, resulting in a slower speed of sound.

This is why sound travels slightly faster on a hot summer day than on a cold winter day.