Sound Waves

Sound waves are longitudinal waves. In air, or any other medium, sound waves are created by a vibrating source.

In which medium does sound travel faster, air or water?

  1. Sound travels faster through air
  2. Sound travels faster through water

The speed of sound

In general, the speed of a mechanical wave is given by:

v = [elastic property / inertial property]½

For a wave on a string, for instance, v = (T/μ)½

For sound waves the inertial factor is the density, ρ.

The relevant elastic property is the bulk modulus, B. This tells us how much a medium's volume changes when the pressure on it changes.

B = -[Δ p/(Δ V/V)]

Note that pressure p is force/unit area.

Therefore the speed of sound is v = (B/ρ)½

The bulk modulus is a measure of how incompressible a material is. The higher the value, the less its volume changes when the pressure changes. Gases generally have small values of B, liquids have higher values, and solids even higher.

Some sample values of the speed of sound are:

Medium Speed of Sound (m/s)
Air (0 degrees C) 331
Air (20 degrees C) 343
Helium 965
Water 1402
Aluminum 6420
Steel 5941

The range of human hearing

Humans are sensitive to a particular range of frequencies, typically from 20 Hz to 20000 Hz. Whether you can hear a sound also depends on its intensity - we're most senstive to sounds of a couple of thousand Hz, and considerably less sensitive at the extremes of our frequency range.

We generally lose the top end of our range as we age.

Other animals are sensitive to sounds at lower or higher frequencies. Anything less than the 20 Hz that marks the lower range of human hearing is classified as infrasound - elephants, for instance, communicate using low frequency sounds. Anything higher than 20 kHz, our upper limit, is known as ultrasound. Dogs, bats, dolphins, and other animals can hear sounds in this range.