Acoustics - How it works

Wave Motion and Sound waves

Sound waves are an example of a larger phenomenon known as wave motion, and wave motion is, in turn, a subset of harmonic motion—that is, repeated movement of a particle about a position of equilibrium, or balance. In the case of sound, the "particle" is not an item of matter, but of energy, and wave motion is a type of harmonic movement that carries energy from one place to another without actually moving any matter.

Particles in waves experience oscillation, harmonic motion in one or more dimensions. Oscillation itself involves little movement, though some particles do move short distances as they interact with other particles. Primarily, however, it involves only movement in place. The waves themselves, on the other hand, move across space, ending up in a position different from the one in which they started.

A transverse wave forms a regular up-and-down pattern in which the oscillation is perpendicular to the direction the wave is moving. This is a fairly easy type of wave to visualize: imagine a curve moving up and down along a straight line. Sound waves, on the other hand, are longitudinal waves, in which oscillation occurs in the same direction as the wave itself.

These oscillations are really just fluctuations in pressure. As a sound wave moves through a medium such as air, these changes in pressure cause the medium to experience alternations of density and rarefaction (a decrease in density). This, in turn, produces vibrations in the human ear or in any other object that receives the sound waves.

Properties of Sound Waves

CYCLE AND PERIOD.

The term cycle has a definition that varies slightly, depending on whether the type of motion being discussed is oscillation, the movement of transverse waves, or the motion of a longitudinal sound wave. In the latter case, a cycle is defined as a single complete vibration.

A period (represented by the symbol T ) is the amount of time required to complete one full cycle. The period of a sound wave can be mathematically related to several other aspects of wave motion, including wave speed, frequency, and wavelength.

THE SPEED OF SOUND IN VARIOUS MEDIA.

People often refer to the "speed of sound" as though this were a fixed value like the speed of light, but, in fact, the speed of sound is a function of the medium through which it travels. What people ordinarily mean by the "speed of sound" is the speed of sound through air at a specific temperature. For sound

B ECAUSE THE SOUND GENERATED BY A JET ENGINE CAN DAMAGE A PERSON ' S HEARING , AIRPORT GROUND CREWS ALWAYS WEAR PROTECTIVE HEADGEAR . (Photograph by

Patrick Bennett/Corbis

. Reproduced by permission.)

In the essay on aerodynamics, the speed of sound for aircraft was given at 660 MPH (451 m/s). This is much less than the figures given above for the speed of sound through air at sea level, because obviously, aircraft are not flying at sea level, but well above it, and the air through which they pass is well below freezing temperature.

The speed of sound through a gas is proportional to the square root of the pressure divided by the density. According to Gay-Lussac's law, pressure is directly related to temperature, meaning that the lower the pressure, the lower the temperature—and vice versa. At high altitudes, the temperature is low, and, therefore, so is the pressure; and, due to the relatively small gravitational pull that Earth exerts on the air at that height, the density is also low. Hence, the speed of sound is also low.

It follows that the higher the pressure of the material, and the greater the density, the faster sound travels through it: thus sound travels faster through a liquid than through a gas. This might seem a bit surprising: at first glance, it would seem that sound travels fastest through air, but only because we are just more accustomed to hearing sounds that travel through that medium. The speed of sound in water varies from about 3,244 MPH (1,450 m/s) to about 3,355 MPH (1500 m/s). Sound travels even faster through a solid—typically about 11,185 MPH (5,000 m/s)—than it does through a liquid.

FREQUENCY.

Frequency (abbreviated f ) is the number of waves passing through a given point during the interval of one second. It is measured in Hertz (Hz), named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894) and a Hertz is equal to one cycle of oscillation per second. Higher frequencies are expressed in terms of kilohertz (kHz; 10 ³ or 1,000 cycles per second) or megahertz (MHz; 10 ⁶ or 1 million cycles per second.)

The human ear is capable of hearing sounds from 20 to approximately 20,000 Hz—a relatively small range for a mammal, considering that bats, whales, and dolphins can hear sounds at a frequency up to 150 kHz. Human speech is in the range of about 1 kHz, and the 88 keys on a piano vary in frequency from 27 Hz to 4,186 Hz. Each note has its own frequency, with middle C (the "white key" in the very middle of a piano keyboard) at 264 Hz. The quality of harmony or dissonance when two notes are played together is a

P IANO STRINGS GENERATE SOUND AS THEY ARE SET INTO VIBRATION BY THE HAMMERS . T HE HAMMERS , IN TURN , ARE ATTACHED TO THE BLACK - AND - WHITE KEYS ON THE OUTSIDE OF THE PIANO . (Photograph by

Bob Krist/Corbis

. Reproduced by permission.)

Frequencies below the range of human audibility are called infrasound, and those above it are referred to as ultrasound. There are a number of practical applications for ultrasonic technology in medicine, navigation, and other fields.

WAVELENGTH.

Wavelength (represented by the symbol λ, the Greek letter lambda) is the distance between a crest and the adjacent crest, or a trough and an adjacent trough, of a wave. The higher the frequency, the shorter the wavelength, and vice versa. Thus, a frequency of 20 Hz, at the bottom end of human audibility, has a very large wavelength: 56 ft (17 m). The top end frequency of 20,000 Hz is only 0.67 inches (17 mm).

There is a special type of high-frequency sound wave beyond ultrasound: hypersound, which has frequencies above 10 ⁷ MHz, or 10 trillion Hz. It is almost impossible for hypersound waves to travel through all but the densest media, because their wavelengths are so short. In order to be transmitted properly, hypersound requires an extremely tight molecular structure; otherwise, the wave would get lost between molecules.

Wavelengths of visible light, part of the electromagnetic spectrum, have a frequency much higher even than hypersound waves: about 10 ⁹ MHz, 100 times greater than for hypersound. This, in turn, means that these wavelengths are incredibly small, and this is why light waves can easily be blocked out by using one's hand or a curtain.

The same does not hold for sound waves, because the wavelengths of sounds in the range of human audibility are comparable to the size of ordinary objects. To block out a sound wave, one needs something of much greater dimensions—width, height, and depth—than a mere cloth curtain. A thick concrete wall, for instance, may be enough to block out the waves. Better still would be the use of materials that absorb sound, such as cork, or even the use of machines that produce sound waves which destructively interfere with the offending sound.

AMPLITUDE AND INTENSITY.

Amplitude is critical to the understanding of sound, though it is mathematically independent from the parameters so far discussed. Defined as the maximum displacement of a vibrating material, amplitude is the "size" of a wave. The greater the amplitude, the greater the energy the wave

T HE HUMAN VOICE , WHETHER IN SPEECH OR IN SONG , IS A REMARKABLE SOUND - PRODUCING INSTRUMENT : AT ANY GIVEN MOMENT AS A PERSON IS TALKING OR SINGING , PARTS OF THE VOCAL CORDS ARE OPENED , AND PARTS ARE CLOSED . S HOWN HERE IS OPERA SUPERSTAR J OAN S UTHERLAND . (

Hulton-Deutsch Collection/Corbis

. Reproduced by permission.)

Intensity can be measured in watts per square meter, or W/m ² . A sound wave of minimum intensity for human audibility would have a value of 10 ⁻¹² , or 0.000000000001, W/m ² . As a basis of comparison, a person speaking in an ordinary tone of voice generates about 10 ⁻⁴ , or 0.0001, watts. On the other hand, a sound with an intensity of 1 W/m ² would be powerful enough to damage a person's ears.