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. Sirens emit sound by means of an air blast interrupted by a toothed wheel with 44 teeth. The wheel rotates at 10 revolutions per second to produce 440 interruptions in the air stream every second. Similarly, hitting the A above middle C on a piano causes a string to vibrate at 440 Hz. The sound of the speaker and that of the piano string at the same frequency are different in quality, but correspond closely in pitch. The next higher A on the piano, the note one octave above, has a frequency of 880 Hz, exactly twice as high. Similarly, the notes one and two octaves below have frequencies of 220 and 110 Hz, respectively. Thus, by definition, an octave is the interval between any two notes whose frequencies are in a two-to-one ratio.

A fundamental law of harmony states that two notes an octave apart, when sounded together, produce a pleasant-sounding combination. Other combinations of notes can also be pleasing. Physically, an interval of a fifth consists of two notes, the frequencies of which bear the arithmetical ratio 3 to 2, and a major third, the ratio 5 to 4. Fundamentally, the law of harmony states that two or more notes sound pleasant when played together if their frequencies bear small, whole number ratios; if the frequencies do not bear such ratios, the intervals are dissonant. On a fixed-pitch instrument, such as the piano, it is not possible to arrange the notes so that all of these ratios hold exactly, and some compromise is necessary in tuning.

B.

Amplitude

The amplitude of a sound wave is the degree of motion of air molecules within the wave, which corresponds to the changes in air pressure that accompany the wave. The greater the amplitude of the wave, the harder the molecules strike the eardrum 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, the changes in pressure as the wave passes, or the energy contained in the wave. 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. Intensity is the average rate of flow of energy per unit area perpendicular to the direction of propagation, similar to the rate at which a river flows through a gate in a dam. In the case of spherical sound waves spreading from a point source, the intensity varies inversely as the square of the distance, provided there is no loss of energy due to viscosity, heat conduction, or other absorption effects. Thunder, for example, is four times as intense at a distance of 1 km (0.6 mi) from the lightning bolt that caused it as it would be at a distance of 2 km (1.2 mi). 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 different in quality. Of these three sources, the simplest tone is produced by the tuning fork; the sound in this case consists almost entirely of vibrations having frequencies of 440 Hz. Because of the acoustical properties of the ear and the resonance properties of the ear's vibrating membrane, however, it is doubtful that 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 Hz, but these notes also contain components with frequencies that are exact multiples of 440, called overtones, at 880, 1320, and 1760 Hz, for example. The exact intensity of these other components, which are called harmonics, determines the quality, or timbre, of the note.

E.

Speed of Sound

The frequency of a sound wave is a measure of the number of waves passing a given point in one second. The distance between two successive crests of the wave is called the wavelength. The product of the wavelength and the frequency equals the speed of the wave. The speed is the same for sounds of all frequencies and wavelengths (assuming the sound is propagated through the same medium at the same temperature). The wavelength of A above middle C, for example, is about 78 cm (about 2.6 ft), and its frequency is 440 Hz. The wavelength of A below middle C is twice as large, about 156 cm (about 5.1 ft), but its frequency, 220 Hz, is only half as large. The product of the wavelengths and frequencies for each note is the same, so the speed of sound is also the same.

The speed of sound in dry, sea level air at a temperature of 0°C (32°F) is 332 m/sec (1,088 ft/sec). The speed of sound in air varies under different conditions. If the temperature is increased, for example, the speed of sound increases; thus, at 20°C (68°F), the speed of sound is 344 m/sec (1,129 ft/sec). The speed of sound is different in other gases of greater or lesser density than air. The molecules of some gases, such as carbon dioxide, are heavier and move less readily than molecules of air. Sound progresses through such gases more slowly. Conversely, sound travels through helium and hydrogen faster than through air because atoms of helium and hydrogen are lighter than molecules of air. Stated mathematically, the speed of sound varies inversely as the square root of the density. The speed of sound in gases also depends on one other factor, specific heat. See Temperature.

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. The speed of sound also varies directly as the square root of the elasticity of the medium. Elasticity is the ability of a substance to regain its original shape and size after being deformed. The speed of sound in water, for example, is slightly less than 1,525 m/sec (5,000 ft/sec) at ordinary temperatures—almost five times as fast as in air. The speed of sound in copper, which is more elastic than water, is about 3,350 m/sec (about 11,000 ft/sec) at ordinary temperatures. In steel, which is even more elastic, sound moves at a speed of about 4,880 m/sec (about 16,000 ft/sec). Sound is propagated very efficiently in steel.

F.

Refraction, Reflection, and Interference

Sound moves forward in a straight line when traveling through a medium having uniform density. Like light, however, sound is subject to refraction, which bends sound waves from their original path. In polar regions, where air close to the ground is colder than air that is somewhat higher, a rising sound wave entering the warmer less dense region, in which sound moves with greater speed, is bent downward 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 meters than near the ground; a rising sound wave moving downwind is bent back toward the ground, whereas a similar sound wave moving upwind is bent upward 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.