### Acoustics

Acoustics is the science of sound waves. Sound consists of molecular vibrations at audio frequency (AF), ranging from about 20 Hz to 20 kHz. Young people can hear the full range of AF; older people lose hearing sensitivity at the upper and lower extremes.

#### Audio Frequencies

In music, the AF range is divided into three broad, vaguely defined parts, called bass (pronounced “base”), midrange, and treble. The bass frequencies start at 20 Hz and extend to 150 or 200 Hz. Midrange begins at this point, and extends up to 2 or 3 kHz. Treble consists of the audio frequencies higher than midrange. As the frequency increases, the wavelength becomes shorter. In air, sound travels at about 1100 feet per second (ft/s), or 335 meters per second (m/s). The relationship between the frequency f of a sound wave in hertz, and the wavelength λft in feet, is as follows:
λft = 1100/f
The relationship between f in hertz and λm in meters is given by:
λm = 335/f
This formula is also valid for frequencies in kilohertz and wavelengths in millimeters. A sound disturbance in air at 20 Hz has a wavelength of 55 ft (17 m). A sound of 1.0 kHz produces a wave measuring 1.1 ft (34 cm). At 20 kHz, a sound wave in air is only 0.055 ft (17 mm) long. In substances other than air at sea level, such as air at extreme altitudes, freshwater, saltwater, or metals, the preceding formulas do not apply.

#### Waveforms

The frequency, or pitch, of a sound is only one of several variables that acoustic waves can possess. Another important factor is the shape of the wave itself. The simplest acoustic waveform is a sine wave (or sinusoid ), in which all of the energy is concentrated at a single frequency. Sinusoidal sound waves are rare in nature. A good artificial example is the beat note, or heterodyne, produced by a steady carrier in a communications receiver.

In music, most of the notes are complex waveforms, consisting of energy at a specific fundamental frequency and its harmonics. Examples are sawtooth, square, and triangular waves. The shape of the waveform depends on the distribution of energy among the fundamental and the harmonics. There are infinitely many different shapes that a wave can have at a single frequency such as 1 kHz. As a result, there is infinite variety in the timbre that a single musical note can have.

#### Path Effects

Sounds from reflected paths (such as X, Y, and Z) combine with direct-path sound (D) to produce what a listener hears.
A flute, a clarinet, a guitar, and a piano can each produce a sound at 1 kHz, but the tone quality is different for each instrument. The waveform affects the way a sound is reflected from objects. Acoustics engineers must consider this when designing sound systems and concert halls. The goal is to make sure that all the instruments sound realistic everywhere in the room.

Suppose you have a sound system set up in your living room, and that, for the particular placement of speakers with respect to your ears, sounds propagate well at 1, 3, and 5 kHz, but poorly at 2, 4, and 6 kHz. This affects the way musical instruments sound. It distorts the sounds from some instruments more than the sounds from others. Unless all sounds, at all frequencies, reach your ears in the same proportions that they come from the speakers, you do not hear the music the way it originally came from the instruments.

Above figure shows a listener, a speaker, and three sound reflectors, also known as baffles. The waves reflected by the baffles (X, Y, and Z), along with the direct-path waves (D), add up to some thing different, at the listener’s ears, for each frequency of sound. This phenomenon is impossible to prevent. That is why it is so difficult to design an acoustical room, such as a concert auditorium, to propagate sound well at all frequencies for every listener.