Understanding Sound Waves and How They Work

There are many sources of sound. Familiar kinds include the vibration of a person's vocal cords, vibrating strings (piano, violin), a vibrating column of air (trumpet, flute), and vibrating solids (a door when someone knocks). It's impossible to list them all because anything that imparts a disturbance to an elastic medium is a source of sound.

Sound can be described in terms of pitch — from the low rumble of distant thunder to the high-pitched buzzing of a mosquito — and loudness. Pitch and loudness, however, are subjective qualities; they depend in part on the hearer's sense of hearing. Objective, measurable qualities of sound include frequency and intensity, which are related to pitch and loudness. These terms, as well as others used in discussing sound, are best understood through an examination of sound waves and their behavior.

Speed of sound in various mediums

Air, like all matter, consists of molecules. Even a tiny region of air contains vast numbers of air molecules. The molecules are in constant motion, traveling randomly and at great speed. They constantly collide with and rebound from one another and strike and rebound from objects that are in contact with the air.

When an object vibrates it produces sound waves in the air. For example, when the head of a drum is hit with a mallet, the drumhead vibrates and produces sound waves. The vibrating drumhead produces sound waves because it moves alternately outward and inward, pushing against, then moving away from, the air next to it. The air particles that strike the drumhead while it is moving outward rebound from it with more than their normal energy and speed, having received a push from the drumhead.

These faster-moving molecules move into the surrounding air. For a moment, the region next to the drumhead has a greater-than-normal concentration of air molecules — it becomes a region of compression. As the faster-moving molecules overtake the air molecules in the surrounding air, they collide with them and pass on their extra energy. The region of compression moves outward as the energy from the vibrating drumhead is transferred to groups of molecules farther and farther away.

Air molecules that strike the drumhead while it's moving inward rebound from it with less than their normal energy and speed. For a moment, the region next to the drumhead has fewer air molecules than normal — it becomes a region of rarefaction. Molecules colliding with these slower-moving molecules also rebound with less speed than normal, and the region of rarefaction travels outward.

The wave nature of sound becomes apparent when a graph is drawn to show the changes in the concentration of air molecules at some point as the alternating pulses of compression and rarefaction pass that point. The graph for a single pure tone, such as that produced by a vibrating tuning fork, would show a sine wave (illustrated here). The curve shows the changes in concentration. It begins, arbitrarily, at some time when the concentration is normal and a compression pulse is just arriving. The distance of each point on the curve from the horizontal axis indicates how much the concentration varies from normal.

Each compression and the following rarefaction make up one cycle. (A cycle can also be measured from any point on the curve to the next corresponding point.) The frequency of a sound is measured in cycles per second or hertz (abbreviated Hz). The amplitude is the greatest amount by which the concentration of air molecules varies from the normal.

The wavelength of a sound is the distance the disturbance travels during one cycle. It's related to the sound's speed and frequency by the formula speed/frequency = wavelength. This means that high-frequency sounds have short wavelengths and low-frequency sounds have long wavelengths. The human ear can detect sounds with frequencies as low as 20 Hz and as high as 20,000 Hz. In still air at room temperature, sounds with these frequencies have wavelengths of 75 feet (23 m) and 0.68 inch (1.7 cm) respectively.

Intensity refers to the amount of energy transmitted by the disturbance. It's proportional to the square of the amplitude. Intensity is measured in watts per square centimeter or in decibels (db). The decibel scale is defined as follows: An intensity of 10-16 watts per square centimeter equals 0 db. (Written out in decimal form, 10-16 appears as 0.0000000000000001.) Each tenfold increase in watts per square centimeter means an increase of 10 db. Thus, an intensity of 10-15 watts per square centimeter can also be expressed as 10 db and an intensity of 10-4 (or 0.0001) watts per square centimeter as 120 db.

The intensity of sound drops rapidly with increasing distance from the source. For a small sound source radiating energy uniformly in all directions, intensity varies inversely with the square of the distance from the source. That is, at a distance of two feet from the source the intensity is one-fourth as great as it is at a distance of one foot; at three feet it is only one-ninth as great as at one foot, etc.

Pitch

Pitch depends on the frequency; in general, a rise in frequency causes a sensation of rising pitch. The ability to distinguish between two sounds that are close in frequency, however, decreases in the upper and lower parts of the audible frequency range. There is also variation from person to person in the ability to distinguish between two sounds of very nearly the same frequency. Some trained musicians can detect differences in frequency as small as 1 or 2 Hz.

Because of how the hearing mechanism functions, the perception of pitch is also affected by intensity. Thus, when a tuning fork vibrating at 440 Hz (the frequency of A above middle C on the piano) is brought closer to the ear, a slightly lower tone, as though the fork were vibrating more slowly, is heard.

When the source of a sound is moving at a relatively high speed, a stationary listener hears a sound higher in pitch when the source is moving toward him or her and a sound lower in pitch when the source is moving away. This phenomenon, known as the Doppler effect, is due to the wave nature of sound.

Loudness

In general, an increase in intensity will cause a sensation of increased loudness. But loudness does not increase in direct proportion to intensity. A sound of 50 dB has ten times the intensity of a sound of 40 dB but is only twice as loud. Loudness doubles with each increase of 10 dB in intensity.

Loudness is also affected by frequency because the human ear is more sensitive to some frequencies than to others. The threshold of hearing — the lowest sound intensity that will produce the sensation of hearing for most people — is about 0 dB in the 2,000 to 5,000 Hz frequency range. For frequencies below and above this range, sounds must have greater intensity to be heard. Thus, for example, a sound of 100 Hz is barely audible at 30 dB; a sound of 10,000 Hz is barely audible at 20 dB. At 120 to 140 dB, most people experience physical discomfort or actual pain, and this level of intensity is referred to as the threshold of pain.

The speed of sound depends on the elasticity and density of the medium through which it is traveling. In general, sound travels faster in liquids than in gases and faster in solids than in liquids. The greater the elasticity and the lower the density, the faster sound moves in a medium. The mathematical relationship is speed = (elasticity/density).

The effect of elasticity and density on the speed of sound can be seen by comparing the speed of sound in air, hydrogen, and iron. Air and hydrogen have nearly the same elastic properties, but the density of hydrogen is less than that of air. Sound travels faster (about 4 times as fast) in hydrogen than in air. Although the density of air is much less than that of iron, the elasticity of iron is very much greater than that of air. Sound travels faster (about 14 times as fast) in iron than in air.

The speed of sound in a material, particularly in a gas or liquid, varies with temperature because a change in temperature affects the material's density. In air, for example, the speed of sound increases with an increase in temperature. At 32 °F. (0 °C.), the speed of sound in air is 1,087 feet per second (331 m/s); at 68 °F. (20 °C.), it is 1,127 feet per second (343 m/s).

The terms subsonic and supersonic refer to the speed of an object, such as an airplane, in relation to the speed of sound in the surrounding air. A subsonic speed is below the speed of sound; a supersonic speed is above the speed of sound. An object traveling at supersonic speed produces shock waves rather than ordinary sound waves. A shock wave is a compression wave that, when produced in air, can usually be heard as a sonic boom.

The speeds of supersonic objects are often expressed in terms of Mach number — the ratio of the object's speed to the speed of sound in the surrounding air. Thus, an object traveling at Mach 1 is traveling at the speed of sound; at Mach 2, it is traveling at twice the speed of sound.

Like light waves and other waves, sound waves are reflected, refracted, and diffracted, and exhibit interference.

Reflection

Sound is constantly being reflected off many different surfaces. Most of the time the reflected sound is not noticed, because two identical sounds that reach the human ear less than 1/15 of a second apart cannot be distinguished as separate sounds. When the reflected sound is heard separately, it's called an echo.

Sound is reflected from a surface at the same angle at which it strikes the surface. This fact makes it possible to focus sound by means of curved reflecting surfaces in the same way that curved mirrors can be used to focus light. It also accounts for the effects of so-called whispering galleries, rooms in which a word whispered at one point can be heard distinctly at some other point fairly far away, though it cannot be heard anywhere else in the room. (The National Statuary Hall of the United States Capitol is an example.) Reflection is also used to focus sound in a megaphone and when calling through cupped hands.

The reflection of sound can pose a serious problem in concert halls and auditoriums. In a poorly designed hall, a speaker's first word may reverberate (echo repeatedly) for several seconds, so that the listeners may hear all the words of a sentence echoing at the same time. Music can be similarly distorted. Such problems can usually be corrected by covering reflecting surfaces with sound-absorbing materials such as draperies or acoustical tiles. Clothing also absorbs sound; for this reason, reverberation is greater in an empty hall than in one filled with people. All these sound-absorbing materials are porous; sound waves entering the tiny air-filled spaces bounce around in them until their energy is spent. They are, in effect, trapped.

The reflection of sound is used by some animals, notably bats, for echolocation — locating, and in some cases identifying, objects through the sense of hearing rather than the sense of sight. Bats emit bursts of sound of frequencies far beyond the upper limits of human hearing. Sounds with short wavelengths are reflected even from very small objects. A bat can unerringly locate and catch even a mosquito in total darkness. Sonar is an artificial form of echolocation.

Refraction

When a wave passes from one material to another at an angle, it usually changes speed, causing the wave front to bend. The refraction of sound can be demonstrated in a physics laboratory by using a lens-shaped balloon filled with carbon dioxide to bring sound waves to a focus.

Diffraction

When sound waves pass around an obstacle or through an opening in an obstacle, the edge of the obstacle or the opening acts as a secondary sound source, sending out waves of the same frequency and wavelength (but of lower intensity) as the original source. The spreading out of sound waves from the secondary source is called diffraction. Because of this phenomenon, sound can be heard around corners despite the fact that sound waves generally travel in a straight line.

Interference

Whenever waves interact, interference occurs. For sound waves, the phenomenon is perhaps best understood by thinking in terms of the compressions and rarefactions of the two waves as they arrive at some point. When the waves are in phase so that their compressions and rarefactions coincide, they reinforce each other (constructive interference). When they are out of phase, so that the compressions of one coincide with the rarefactions of the other, they tend to weaken or even cancel each other (destructive interference). The interaction between the two waves produces a resultant wave.

In auditoriums, destructive interference between sound from the stage and sound reflected from other parts of the hall can create dead spots in which both the volume and clarity of sound are poor. Such interference can be reduced by the use of sound-absorbing materials on reflecting surfaces. On the other hand, interference can improve an auditorium's acoustical qualities. This is done by arranging the reflecting surfaces in such a way that the level of sound is actually increased in the area in which the audience sits.

Interference between two waves of nearly but not quite equal frequencies produces a tone of alternately increasing and decreasing intensity because the two waves continually fall in and out of phase. The pulsations heard are called beats. Piano tuners make use of this effect, adjusting the tone of a string against that of a standard tuning fork until beats can no longer be heard.

Sounds of a single pure frequency are produced only by tuning forks and electronic devices called oscillators; most sounds are a mixture of tones of different frequencies and amplitudes. The tones produced by musical instruments have one important characteristic in common: they are periodic, that is, the vibrations occur in a repeating pattern. The oscilloscope trace of a trumpet's sound shows such a pattern. For most non-musical sounds, such as those of a bursting balloon or a person coughing, an oscilloscope trace would show a jagged, irregular pattern, indicating a jumble of frequencies and amplitudes.

A column of air, as that in a trumpet, and a piano string both have a fundamental frequency — the frequency at which they vibrate most readily when set in motion. For a vibrating column of air, that frequency is determined principally by the length of the column. (The trumpet's valves are used to change the effective length of the column.) For a vibrating string, the fundamental frequency depends on the string's length, its tension, and its mass per unit length.

In addition to its fundamental frequency, a string or vibrating column of air also produces overtones with frequencies that are whole-number multiples of the fundamental frequency. It is the number of overtones produced and their relative strength that gives a musical tone from a given source its distinctive quality or timbre. The addition of further overtones would produce a complicated pattern, such as that of the oscilloscope trace of the trumpet's sound.

How the fundamental frequency of a vibrating string depends on the string's length, tension, and mass per unit length is described by three laws:

1. The fundamental frequency of a vibrating string is inversely proportional to its length.

Reducing the length of a vibrating string by one-half will double its frequency, raising the pitch by one octave, if the tension remains the same.

2. The fundamental frequency of a vibrating string is directly proportional to the square root of the tension.

Increasing the tension of a vibrating string raises the frequency; if the tension is made four times as great, the frequency is doubled, and the pitch is raised by one octave.

3. The fundamental frequency of a vibrating string is inversely proportional to the square root of the mass per unit length.

This means that of two strings of the same material and with the same length and tension, the thicker string has the lower fundamental frequency. If the mass per unit length of one string is four times that of the other, the thicker string has a fundamental frequency one-half that of the thinner string and produces a tone one octave lower.

One of the first discoveries regarding sound was made in the sixth century B.C. by the Greek mathematician and philosopher Pythagoras. He noted the relationship between the length of a vibrating string and the tone it produces — what is now known as the first law of strings. Pythagoras may also have understood that the sensation of sound is caused by vibrations. Not long after his time it was recognized that this sensation depends on vibrations traveling through the air and striking the eardrum.

About 1640 the French mathematician Marin Mersenne conducted the first experiments to determine the speed of sound in air. Mersenne is also credited with discovering the second and third laws of strings. In 1660 the British scientist Robert Boyle demonstrated that the transmission of sound required a medium — by showing that the ringing of a bell in a jar from which the air had been pumped could not be heard.

Ernst Chladni, a German physicist, made extensive analyses of sound vibrations during the late 1700s and early 1800s. In the early 1800s, the French mathematician Fourier discovered that such complex waves as those produced by a vibrating string with all its overtones consist of a series of simple periodic waves.

An important contribution to the understanding of acoustics was made by Wallace Clement Sabine, a physicist at Harvard University, in the late 1890s. Sabine was asked to improve the acoustics of the main lecture hall in Harvard's Fogg Art Museum. He was first to measure reverberation time — which he found to be 5 1/2 seconds in the lecture hall. Experimenting first with seat cushions from a nearby theater, and later with other sound-absorbing materials and other methods, Sabine laid the foundation for architectural acoustics. He designed Boston Symphony Hall (opened in 1900), the first building with scientifically formulated acoustics.

In the second half of the 20th century, the rising level of noise in the modern world — particularly in urban areas — prompted a whole new series of investigations, dealing in large part with the physiological and psychological effects of noise on humans.

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.