Music and Sound Waves

All material substances are comprised of atoms, which may be forced into oscillations about their equilibrium positions. Many different patterns of vibration exist at the atomic level and acoustics is focused on particles that contain atoms that move in unison to produce a mechanical wave. When the particles of a medium are displaced from their equilibrium positions, internal (electrostatic) restoration forces arise. It is these elastic restoring forces between particles, combined with inertia of the particles, that produces oscillatory motions of the medium. In air, sound travels by compression and expansion of air molecules in the direction of travel. The oscillations occur in the direction of the propagation and since compressive and expansive forces are active in these waves, they are also called pressure or compression waves. In some instances they are called density waves because their particle density fluctuates as they move. Compression waves can be generated in liquids, as well as solids because the energy travels through the atomic structure by a series of compression and expansion movements.

Sound Wave Propagation Animation

Sound waves have three properties, the speed in which they travel, their amplitude and frequency. The arrangement of these characteristics is key to understanding the phenomena associated with them. The speed of sound in air is temperature dependant and is given by the following relationship,

(1)

where c is the speed of sound P is pressure and is the density. For an ideal gas the relationship can be extended so that the product of the pressure and specific volume is equivalent to the product of the gas constant R and the temperature T. This relationship is maintained when the pressure increase propagates through the medium, similar to the domino effect. The density of the medium increases, keeping the ratio constant. Sounds are characterized by their volume, which is the amplitude of the pressure disturbance, and their pitch or the frequency of oscillation. The volume of sound waves is commonly denoted in units of decibels where the decibel is given by,

(2)

The reference pressure is the smallest audible pressure wave amplitude distinguishable by the human ear. The following figure shows the amplitudes of sounds encountered by most people to give an intuitive reference for the decibel unit.