WAVES

Waves which are involved in many aspects of life, are disturbances that propagate through a medium with a definite speed. A wave of light conveys information to the eyes, a wave of sound brings music to the ears, a water wave rolling onto a beach can topple the swimmer, and electromagnetic waves cook food (microwave oven), and carry television reception. It takes energy to create the wave disturbance, and how the wave travels through the medium (elastic or damped) is quite variable.

There are two important categories of waves, mechanical and electromagnetic. Mechanical waves require a material medium. Water waves in a pond require water, sound waves in a room require air, a stadium "wave" must have people, and a wave produced by plucking a guitar string needs a string. Mechanical waves are produced when the medium is disturbed. A stone dropped in a pond disturbs the water, a spoken word results from a pressure disturbance, the guitar player disturbs the string by plucking it, and the sports fan disturbs the audience by standing up. The disturbance moves through the medium with a speed that is determined by the properties of the medium. In a stringed musical instrument, for example, the mass of the string and how tightly it is stretched determine the speed. That is why there are different size strings and a mechanism for tightening them.

A stone dropped in a pond pushes the water downward, which is countered by elastic forces in the water that tend to restore the water to its initial condition. The movement of the water is up and down, but the crest of the wave produced moves along the surface of the water. This type of wave is said to be transverse because the displacement of the water is perpendicular to the direction the wave moves. When the oscillations of the wave die out, there has been no net movement of water; the pond is just as it was before the stone was dropped. Yet the wave has energy associated with it. A person has only to get in the path of a water wave crashing onto a beach to know that energy is involved. The stadium wave is a transverse wave, as is a wave in a guitar string.

When air in a room is disturbed by a person speaking the molecules of the air have movements that are along the path of the wave. If you were to draw a line from the speaker's mouth to your ear, the movement of the molecules would be along this line. This type of wave, called an acoustical wave, is said to be longitudinal. The pleasant sounds of music are produced by acoustical waves. On the other hand, destruction by a bomb blast also is caused by acoustical waves. Instead of oscillating up and down, molecules in the acoustical (or compression) wave bunch together as the wave passes. It is not a transverse wave.

Imagine something floating in a pan of water with both the float and the water motionless (Figure 1A). If you were to continually bob the float up and down, you would see a continuous train of crests and troughs moving away from the float (Figure 1B). The separation of adjacent crests is called the wavelength, and given the lower case Greek lambda (?) for a symbol. The time it takes one of the crests to travel a distance equal to the wavelength is called the period, and given the symbol T. The speed that the crest moves is just the distance traveled divided by the time so that v = 1/T. The period measured in seconds is just the time for one cycle of the oscillation. The reciprocal of the period is the number of cycles per second and is called the frequency, symbol f. The speed of the wave can also be written v = f ?.This simple relationship is a very important feature of all types of waves.

When waves encounter something in their path, they may bounce off (reflect) somewhat like a ball bouncing off a wall. A sound echo is produced by sound waves reflecting from something, a building, for example. We see our image in a mirror because of reflection of light. Reflection as well as other phenomena involving light led to the notion that light is a wave. It is decidedly different from a sound wave because there is no material medium required to sustain its motion. Light traveling to Earth from a distant star encounters virtually no matter until it reaches Earth's atmosphere. Modeling light as a wave has many virtues and uses.

Light is an example of electromagnetic waves. Electromagnetic waves propagate electric and magnetic fields. All electromagnetic waves travel with the same speed in a vacuum. This speed is given the symbol c and has a value 3.00 × 10⁸ m/s (300,000,000 m/s). The general equation v = f ? becomes c = f ? for electromagnetic waves. Because c is the same for all electromagnetic waves in vacuum, f ? is constant. Therefore, when the frequency of an electromagnetic wave increases, the wavelength must decrease. The range of wavelengths of electromagnetic waves is staggering: about 10^-14 m (roughly the diameter of the nucleus of an atom) to about 1,000,000 m (approximately the distance from New York to Chicago). Because f ? is constant, the frequency varies from a high of about 10²² Hz to a low of about 10³ Hz.

Electromagnetic radiation is classified according to ranges of wavelength. Although the classifications are not precise, they are useful. For example, visible light to which our eyes are sensitive has wavelengths between about 4 × 10^-7 m and 7 × 10^-7 m. Microwaves have much longer wavelengths, about 0.001 m to 0.3 m.

Energy streams to Earth from the sun by electro- magnetic waves. Photosynthesis depends on solar energy, and humans and animals rely on photosyn- thesis for food. In this sense, solar energy is not a luxury, it is essential.

All objects, including the sun and incandescent light bulbs, emit electromagnetic radiation. The radiant energy and the type of radiation depend on the temperature. When an electric toaster is switched on, the heating element begins to glow and one can feel the radiant energy increase as the temperature increases. Visible radiation is produced by both the sun and a light bulb because the temperature of both is roughly 6,000 K. When the bulb cools to room temperature, about 300 K, the visible radiation disappears for all practical purposes. Nevertheless, the bulb at 300 K is still radiating, but the radiation is predominantly infrared that our eyes do not sense.

Radiation from the sun includes significant ultra- violet and infrared radiation in addition to visible radiation. Contributions of each type to the radiation that reaches Earth's surface are reduced significantly through absorption in Earth's atmosphere. The rate at which solar radiation falls on a square meter of Earth's solid surface is called the solar insolation. Solar insolation depends on the time of day, the day of the year, and where the square meter is located on Earth's surface. During an eight-hour period, the solar insolation in midwestern United States is roughly 600 W/m². If the 600 watts striking a 1 m² surface could be collected and converted to electricity, there would be enough electricity to operate six typical 100-watt light bulbs.

Solar energy can be used in many ways: heating buildings and houses, providing heat for producing steam for a turbogenerator in an electric power plant, producing electricity with photovoltaic cells, and so on. But since solar energy is not highly concentrated, it takes a considerable area of collection to even heat a small home, which makes it uneconomical and impractical in many situations.

One of the most interesting and fascinating methods of electronic communication uses electromagnetic waves of light. The light is literally piped around in tiny bundles of transparent strings called optical fibers. Because the frequency of the light is thousands of times greater than the frequency of radio and television waves, a much higher concentration of information is permitted. The telephone industry makes great use of transmission of information via optical fibers. Using this technology allows information to be transmitted between North America and Europe via optical fiber cables strung beneath the surface of the Atlantic Ocean.

The back-and-forth motion of a child's swing is an example of an oscillating system, oscillator, for short. Set into motion, these systems oscillate at a frequency determined by properties of the oscillator. For example, the length of a child's swing and the acceleration due to gravity (g) determines the frequency of the back-and-forth motion of a child's swing. Periodically feeding energy into such a system at the same rate as the natural frequency gradually increases the energy of the oscillator. This is the phenomenon of resonance. Children achieve resonance with a swing by "pumping" at the resonant frequency of the swing. Molecules are microscopic oscillators that can be "pumped" by electromagnetic waves. If the frequencies match, the molecules absorb energy. Water molecules have a resonant frequency that falls in the microwave region of the electromagnetic spectrum. Water-based materials exposed to microwaves of the proper frequency absorb energy and heat up. This principle is exploited in a microwave cooker. When food on a plastic plate is placed in a microwave oven. the food warms because of its water content, and the plate does not warm because it is essentially devoid of water.

Ozone is a molecule formed from binding together three oxygen atoms. Gaseous ozone readily absorbs selected frequencies of ultraviolet radiation because ozone molecules have a resonant frequency in the ultraviolet region of the electromagnetic spectrum. A natural concentration of ozone exists twenty to thirty kilometers above Earth's surface. Ozone molecules absorb nearly all ultraviolet radiation from the sun having a wavelength less than about 0.3 micrometers. Accordingly, the natural ozone layer protects humans from harmful effects such as skin cancer. Human-made products migrating into the ozone layer can react with ozone molecules and convert them to other forms that do not absorb ultraviolet radiation. Chlorinated fluorocarbons, CFCs for short, once commonly used in refrigerators and aerosol spray cans, were found to be depleting the ozone, and in 1978 were banned from use in aerosol sprays. Banning the use of CFCs has not totally solved the ozone depletion problem.

Carbon dioxide is a molecule formed from binding together two oxygen atoms and one carbon atom. Gaseous carbon dioxide readily absorbs selected frequencies of infrared radiation because carbon dioxide molecules have a resonant frequency in the infrared region of the electromagnetic spectrum. Coal, natural gas, and oil all have carbon as a component, and carbon dioxide is produced when they are burned. It is a fact that the concentration of carbon dioxide in the atmosphere has been increasing since the Industrial Revolution. The carbon dioxide has little effect on solar radiation penetrating Earth's atmosphere. Earth absorbs the solar energy and, like any object, emits electro- magnetic radiation. The temperature of Earth is more than 5,000 K lower than the sun, and Earth's radiation is mostly infrared. Carbon dioxide can absorb energy from the infrared radiation, resulting in a temperature increase of Earth. This is the socalled "greenhouse effect."

Coping with the greenhouse effect is a very difficult sociopolitical problem. A greenhouse effect existed on Earth long before the Industrial Revolution. Had it not, Earth's surface would be much colder than it is now. The introduction of gases absorbing infrared radiation only enhances the greenhouse effect. Carbon dioxide is not the only gas of importance; water vapor and methane, for example, are also of concern. The industrial world is dependent on coal, oil, and natural gas, so it is not easy to quit burning them to stop producing carbon dioxide.

The radiation one sees from a neon advertising sign or a laser is not produced by accelerated electric charges or by thermal effects. It comes from atoms or molecules that have absorbed energy and given this energy up as photons. A photon is a unit of electro- magnetic energy having energy equal to Planck's constant (6.63 × 10^-34 joule.seconds) times the frequency of the radiation (E = hf ). The frequency of the radiation is determined by the magnitude of energy associated with atoms and molecules. Radiation from atoms and molecules is usually in the infrared, visible, and ultraviolet regions of the electromagnetic spectrum. Electromagnetic radiation also results from energy transitions in the nucleus of an atom. However, the nuclear energy scale is roughly a million times larger, making the frequency of the radiation correspondingly larger. This radiation is called gamma radiation.

All electromagnetic radiation has energy to some extent. Absorption of electromagnetic energy can be put to good use, as in photosynthesis or a microwave oven. On the other hand, electromagnetic energy can do damage. Skin cancer can result from absorption of ultraviolet radiation from the sun. This is why young and old are encouraged to stay out of the summer sun between the hours of 10 A.M. and 2 P.M. Gamma radiation is more energetic and more penetrating than ultraviolet, and the damage it can do is not confined to the surface of the skin. This is why some are concerned about the gamma radiation produced by radioactive nuclei in the spent fuel of a nuclear reactor. Ironically, gamma radiation is used to treat certain types of cancer.

Joseph Priest

See also: Atmosphere; Climatic Effects; Communications and Energy.

BIBLIOGRAPHY

Hobson, A. (1995). Physics: Concepts and Connections. Englewood Cliffs, NJ: Prentice-Hall.

Serway, R. A. (1998). Principles of Physics, 2nd ed. Fort Worth, TX: Saunders College Publishing.