II.

Physical Characteristics

Any simple sound, such as a musical note, may be completely described by specifying three perceptual characteristics: pitch, loudness (or intensity), and quality (or timbre). These characteristics correspond exactly to three physical characteristics: frequency, amplitude, and harmonic constitution, or waveform, respectively. Noise is a complex sound, a mixture of many different frequencies or notes not harmonically related.

A.

Frequency

Sounds can be produced at a desired frequency by different methods. For example, a sound of 440 hertz can be created by actuating a loudspeaker with an oscillator tuned to this frequency (see Sound Recording and Reproduction). An air blast can be interrupted by a toothed wheel with 44 teeth, rotating at 10 revolutions per second; this method is used in operating an ordinary siren. The sound of the speaker and that of the siren at the same frequency are very different in quality, but will correspond closely in pitch, equivalent to the A above middle C on a piano. The next higher A on the piano, the note one octave above, has a frequency of 880 hertz. Similarly, notes one and two octaves below have frequencies of 220 and 110 hertz, respectively. Thus, by definition, an octave is the interval between any two notes the frequencies of which are in a two-to-one ratio.

A fundamental law of harmony states that two notes an octave apart, when sounded together, produce a euphonious combination. A fifth and a major third produce successively less euphonious combinations. Physically, an interval of a fifth is the relationship between two notes, the frequencies of which bear the arithmetical ratio three to two; in a major third, the ratio is five to four. Fundamentally, then, the law of harmony states that two or more notes sound euphonious when played together if their frequencies are in the ratio of small whole numbers; if the frequencies are not in such ratios, a dissonance is produced. On a fixed-pitch instrument, such as a piano, it is not possible to arrange the notes so that all of these ratios hold exactly, and some compromise is necessary in tuning, in accordance with the meantone system, or tempered scale.

B.

Amplitude

The amplitude of a sound wave is the degree of motion of air molecules within the wave, which corresponds to the extent of rarefaction and compression that accompanies the wave. The greater the amplitude of the wave, the harder the molecules strike the ear drum and the louder the sound that is perceived. The amplitude of a sound wave can be expressed in terms of absolute units by measuring the actual distance of displacement of the air molecules, or the pressure differential in the compression and rarefaction, or the energy involved. Ordinary speech, for example, produces sound energy at the rate of about one hundred-thousandth of a watt. All of these measurements are extremely difficult to make, however, and the intensity of sounds is generally expressed by comparing them to a standard sound, measured in decibels (see Sensations of Tone below).

C.

Intensity

The distance at which a sound can be heard depends on its intensity, which is the average rate of flow of energy per unit area perpendicular to the direction of propagation. In the case of spherical waves spreading from a point source, the intensity varies inversely as the square of the distance, provided that no loss of energy is due to viscosity, heat conduction, or other absorption effects. Thus, in a perfectly homogeneous medium, a sound will be nine times as intense at a distance of 1 unit from its origin as at a distance of 3 units; that is, intensity varies inversely as the square of the distance. In the actual propagation of sound through the atmosphere, changes in the physical properties of the air, such as temperature, pressure, and humidity, produce damping and scattering of the directed sound waves, so that the inverse-square law generally is not applicable in direct measurements of the intensity of sound.

D.

Quality

If A above middle C is played on a violin, a piano, and a tuning fork, all at the same volume, the tones are identical in frequency and amplitude, but very different in quality. Of these three sources, the simplest tone is produced by the tuning fork, the sound in this case consisting almost entirely of vibrations having frequencies of 440 hertz. Because of the acoustical properties of the ear and the resonance properties of the ear's vibrating membrane, however, it is doubtful whether a pure tone reaches the inner hearing mechanism in an unmodified form. The principal component of the note produced by the piano or violin also has a frequency of 440 hertz, but these notes also contain components with frequencies that are exact multiples of 440, called overtones, such as 880, 1320, and 1760. The exact intensities of these other components, which are called harmonics, determine the quality of the note.

E.

Velocity of Sound

The frequency of a sound wave is a measure of the number of waves passing a given point in 1 second. The distance between two successive crests of the wave is called the wavelength. The product of the wavelength and the frequency must equal the speed of propagation of the wave, and is the same for sounds of all frequencies (if the sound is propagated through the same medium at the same temperature). Thus, the wavelength of A above middle C is about 78.2 cm (about 2.6 ft), and the wavelength of A below middle C is about 156.4 cm (about 5.1 ft).

The speed of propagation of sound in dry air at a temperature of 0° C (32° F) is 331.6 m/sec (1,088 ft/sec). If the temperature is increased, the speed of sound increases; thus, at 20° C (68° F), the velocity of sound is 344 m/sec (1,129 ft/sec). Changes in pressure at constant density have virtually no effect on the speed of sound. The velocity of sound in many other gases depends only on their density. If the molecules are heavy, they move less readily, and sound progresses through such a medium more slowly. Thus, sound travels slightly faster in moist air than in dry air, because moist air contains a greater number of lighter molecules. The velocity of sound in most gases depends also on one other factor, the specific heat, which affects the propagation of sound waves.

Sound generally moves much faster in liquids and solids than in gases. In both liquids and solids, density has the same effect as in gases; that is, velocity varies inversely as the square root of the density. The velocity also varies directly as the square root of the elasticity. The speed of sound in water, for example, is slightly less than 1,525 m/sec (5,000 ft/sec) at ordinary temperatures but increases greatly with an increase in temperature. The speed of sound in copper is about 3,353 m/sec (11,000 ft/sec) at ordinary temperatures and decreases as the temperature is increased (owing to decreasing elasticity); in steel, which is more elastic, sound moves at a speed of about 4,877 m/sec (about 16,000 ft/sec). Sound is propagated very efficiently in steel.

F.

Refraction, Reflection, and Interference

Sound moves forwards in a straight line when travelling through a medium having uniform density. Like light, however, sound is subject to refraction, the bending of waves from their original path (see Optics). In polar regions, for example, where air close to the ground is colder than air that is somewhat higher, a rising sound wave entering the warmer region, in which sound moves with greater speed, is bent downwards by refraction. The excellent reception of sound downwind and the poor reception upwind are also due to refraction. The velocity of wind is generally greater at an altitude of many metres than near the ground; a rising sound wave moving downwind is bent back towards the ground, whereas a similar sound wave moving upwind is bent upwards over the head of the listener.

Sound is also governed by reflection, obeying the fundamental law that the angle of incidence equals the angle of reflection. An echo is the result of reflection of sound. Sonar depends on the reflection of sounds propagated in water. A megaphone is a funnel-like tube that forms a beam of sound waves by reflecting some of the diverging rays from the sides of the tube. A similar tube can gather sound waves if the large end is pointed at the source of the sound; an ear trumpet is such a device.

Sound is also subject to diffraction and interference. If sound from a single source reaches a listener by two different paths—one direct and the other reflected—the two sounds may reinforce one another; but if they are out of phase they may interfere, so that the resultant sound is actually less intense than the direct sound without reflection. Interference paths are different for sounds of different frequencies, so that interference produces distortion in complex sounds. Two sounds of different frequencies may combine to produce a third sound, the frequency of which is equal to the sum or difference of the original two frequencies.