The Physics of Music

Fluid Behaviors of Sound Waves

Sound is capable of being produced only if a medium is present. By this, I mean that, for there to be sound, there must be air. For a sound wave to be emitted by an instrument and be received by a listener, the instrument must excite the air around it and propagate its energy through the air, in the form of compression/longitudinal waves. When received by the listener, the waves pulse the eardrums with the same varying frequencies as they were emitted.

An instrument shakes to produce its tone

In instruments, air is excited and set into oscillation by vibrations. Instruments use such mechanisms as strings (violin and guitar), bars or rods (marimba and chimes and reeds), membranes (drum heads), plates or shells (cymbals or gongs), air in tubes (woodwinds and brass), or volumes of air enclosed in vessels (drum and string bodies) to produce vibrations.

Sound oscillations are created as the oscillating instrument vibrates a column of air and “bumps” the air that is within immediate proximity. This bump sends out a compression, also called longitudinal, waves in all directions.

The tone of a brass instrument is produced as a player contracts their embouchure and expels a jet of air in order to vibrate their lips, and thereby vibrate the air in the tubing of their horn.

The tone of reed instruments (single or double) is produced by holding a reed rigid and forcing air over, or through. When this happens, the reed vibrates, creating an oscillation.

The tone of flute instruments is produced when air blown over the mouthpiece hole excites surrounding particles. When the vibrations of these surrounding particles match the natural frequency of the instrument, the column of air inside the instrument begins to vibrate, and thus, a tone is produced.

The tone of a string instrument is produced when the string is plucked or drawn by a bow to create a transverse wave (or in the case of the long-bow harp which is drawn to create an internal longitudinal wave).

The path of sound through air

Longitudinal waves describe the path of sound as it is emitted from an instrument. Though the path is longitudinal, sound waves are mathematically expressed as periodic sine waves.

An isolated instrument will produce a wide range of vibrations from its various components. The vibration of the instrument as a whole, however, is considered to be the amalgam of these vibrations—the vibrations of the system.

Clarification of misunderstood terms

Sound: Sound is an effect produced either by mechanical, acoustical, or electrical means. The effect is vibration. The concept of sound is defined by infinite possible vibrations where the ear sets up physiological limits.
Tone: A tone is a purely sinusoidal vibration of air particles in time. The concept of tone is defined by the wider mechanics of the concept of sound, but differs in that the ear sets up musical limits.
Note: A note is defined by a number of tones.
Noise: Any auditory signal.

Three ranges of audio signals

Infrasonic frequencies: The range of frequencies below human capacity for reception. For example, setting a swing set into motion. The swing is oscillating, but we cannot hear its vibration. This is because the frequency of oscillation is below audible human capacity.

Sonic frequencies: The range of frequencies humans can receive.

Ultrasonic frequencies: The range of frequencies above human capacity. For example, turning on a light. The light illuminates an environment, but the frequency it emits is well above what humans can hear.