Wave Motion - Real-life applications

Pulses on a String

There is another variety of wave, though it is defined in terms of behavior rather than the direction of disturbance. (In terms of direction, it is simply a variety of transverse wave.) This is a standing wave, produced by causing vibrations on a string or other piece of material whose ends are fixed in place. Standing waves are really a series of pulses that travel down the string and are reflected back to the point of the original disturbance.

Suppose you hold a string in one hand, with the other end attached to a wall. If you give the string a shake, this causes a pulse—an isolated, non-periodic disturbance—to move down it. A pulse is a single wave, and the behavior of this lone wave helps us to understand what happens within the larger framework of wave motion. As with wave motion in general, the movement of the pulse involves both kinetic and potential energy. The tension of the string itself creates potential energy; then, as the movement of the pulse causes the string to oscillate upward and downward, this generates a certain amount of kinetic energy.

TENSION AND REFLECTION.

The speed of the pulse is a function of the string and its properties, not of the way that the pulse was originally delivered. The tighter the string, and the less its mass per unit of length, the faster the pulse travels down it. The greater the mass per unit of length, however, the greater the inertia resisting the movement of the pulse. Furthermore, the more loosely you hold the string, the less it will respond to the movement of the pulse.

In accordance with the third law of motion, there should be an equal and opposite reaction once the pulse comes into contact with the wall. Assuming that you are holding the string tightly, this reaction will be manifested in the form of an inverted wave, or one that is upside-down in relation to the original pulse. In this case, the tension on the end attached to the support is equal and opposite to the tension exerted by your hand. As a result, the pulse comes back in the same shape as before, but inverted.

If, on the other hand, you hold the other end of the string loosely; instead, once it reaches the wall, its kinetic energy will be converted into potential energy, which will cause the end of the string closest to the wall to move downward. This will result in sending back a pulse that is reversed in horizontal direction, but the same in vertical direction.

In both cases, the energy in the string is reflected backward to its source—that is, to the place from which the pulse was originally produced by the action of your hand. If, however, you hold the string so that its level of tension is exactly between perfect rigidity and perfect looseness, then the pulse will not be reflected. In other words, there will be no reflected wave.

TRANSMISSION AND REFLECTION.

If two strings are joined end-to-end, and a pulse is produced at one end, the pulse would, of course, be transmitted to the second string. If, however, the second string has a greater mass per unit of length than the first one, the result would be two pulses: a transmitted pulse moving in the "right" direction, and a reflected, inverted pulse, moving toward the original source of energy. If, on the other hand, the first string has a greater mass per unit of length than the second one, the reflected pulse would be erect (right side up), not inverted.

For simplicity's sake, this illustration has been presented in terms of a string attached to a wall, but, in fact, transmission and reflection occur in a number of varieties of wave motion— not just those involving pulses or standing waves. A striking example occurs when light hits an ordinary window. The majority of the light, of course, is transmitted through the window pane, but a portion is reflected. Thus, as one looks through the window, one also sees one's reflection.

Similarly, sound waves are reflected depending on the medium with which they are in contact. A canyon wall, for instance, will reflect a great deal of sound, and, thus, it is easy to produce an echo in such a situation. On the other hand, there are many instances in which the desire is to "absorb" sound by transmitting it to some other form of material. Thus, for example, the lobby of an upscale hotel will include a number of plants, as well as tapestries and various wall hangings. In addition to adding beauty, these provide a medium into which the sound of voices and other noises can be transmitted and, thus, absorbed.

Sound Waves

PRODUCTION.

The experience of sound involves production, or the generation of sound waves; transmission, or the movement of those waves from their source; and reception, the principal example of which is hearing. Sound itself is discussed in detail elsewhere. Of primary concern here is the transmission, and to a lesser extent, the production of sound waves.

In terms of production, sound waves are, as noted, longitudinal waves: changes in pressure, or alternations between condensation and rarefaction. Vibration is integral to the generation of sound. When the diaphragm of a loudspeaker pushes outward, it forces nearby air molecules closer together, creating a high-pressure region all around the loudspeaker. The loudspeaker's diaphragm is pushed backward in response, thus freeing up a volume of space for the air molecules. These, then, rush toward the diaphragm, creating a low-pressure region behind the high-pressure one. As a result, the loudspeaker sends out alternating waves of high pressure (condensation) and low pressure (rarefaction).

FREQUENCY AND WAVELENGTH.

As sound waves pass through a medium such as air, they create fluctuations between condensation and rarefaction. These result in pressure changes that cause the listener's eardrum to vibrate with the same frequency as the sound wave, a vibration that the ear's inner mechanisms translate and pass on to the brain. The range of audibility for the human ear is from 20 Hz to 20 kHz. The lowest note of the eighty-eight keys on a piano is 27 Hz and the highest 4.186 kHz. This places the middle and upper register of the piano well within the optimal range for audibility, which is between 3 and 4 kHz.

Sound travels at a speed of about 1,088 ft (331 m) per second through air at sea level, and the range of sound audible to human ears includes wavelengths as large as 11 ft (3.3 m) and as small as 1.3 in (3.3 cm). Unlike light waves, which are very small, the wavelengths of audible sound are comparable to the sizes of ordinary objects. This creates an interesting contrast between the behaviors of sound and light when confronted with an obstacle to their transmission.

It is fairly easy to block out light by simply holding up a hand in front of one's eyes. When this happens, the Sun casts a shadow on the other side of one's hand. The same action does not work with one's ears and the source of a sound, however, because the wavelengths of sound are large enough to go right past a relatively small object such as a hand. However, if one were to put up a tall, wide cement wall between oneself and the source of a sound—as is often done in areas where an interstate highway passes right by a residential community—the object would be sufficiently large to block out much of the sound.

Radio Waves

Radio waves, like visible light waves, are part of the electromagnetic spectrum. They are characterized by relatively long wavelengths and low frequencies—low, that is, in contrast to the much higher frequencies of both visible and invisible light waves. The frequency range of radio is between 10 KHz and about 2,000 MHz—in other words, from 10,000 Hz to as much as 2 billion Hz—an impressively wide range.

AM radio broadcasts are found between 0.6 and 1.6 MHz, and FM broadcasts between 88 and 108 MHz. Thus, FM is at a much, much higher frequency than AM, with the lowest frequency on the FM dial 55 times as great as the highest on the AM dial. There are other ranges of frequency assigned by the FCC (Federal Communications Commission) to other varieties of radio transmission: for instance, citizens' band (CB) radios are in a region between AM and FM, ranging from 26.985 MHz to 27.405 MHz.

Frequency does not indicate power. The power of a radio station is a function of the wattage available to its transmitter: hence, radio stations often promote themselves with announcements such as "operating with 100,000 watts of power…." Thus, an AM station, though it has a much lower frequency than an FM station, may possess more power, depending on the wattage of the transmitter. Indeed, as we shall see, it is precisely because of its high frequency that an FM station lacks the broadcast range of an AM station.

AMPLITUDE AND FREQUENCY MODULATIONS.

What is the difference between AM and FM? Or to put it another way, why is it that an AM station may be heard halfway across the country, yet its sound on a car radio fades out when the car goes under an over-pass? The difference relates to how the various radio signals are modulated.

A radio signal is simply a carrier: it may carry Morse code, or it may carry complex sounds, but in order to transmit voices and music, its signal must be modulated. This can be done, for instance, by varying the instantaneous amplitude of the radio wave, which is a function of the radio station's power. These variations in amplitude are called amplitude modulation, or AM, and this was the first type of commercial radio to appear. Developed in the period before World War I, AM made its debut as a popular phenomenon shortly after the war.

Ironically, FM (frequency modulation) was developed not long after AM, but it did not become commercially viable until well after World War II. As its name suggests, frequency modulation involves variation in the signal's frequency. The amplitude stays the same, and this—combined with the high frequency—produces a nice, even sound for FM radio.

But the high frequency also means that FM signals do not travel as far. If a person is listening to an FM station while moving away from the station's signal, eventually the station will be below the horizon relative to the car, and the car radio will no longer be able to receive the signal. In contrast to the direct, or line-of-sight, transmissions of FM stations, AM signals (with their longer wavelengths) are reflected off of layers in Earth's ionosphere. As a result, a nighttime signal from a "clear channel station" may be heard across much of the continental United States.

WHERE TO LEARN MORE

Ardley, Neil. Sound Waves to Music. New York: Gloucester Press, 1990.

Berger, Melvin and Gilda Berger. What Makes an Ocean Wave?: Questions and Answers About Oceans and Ocean Life. New York: Scholastic, 2001.

Catherall, Ed. Exploring Sound. Austin, TX: Steck-Vaughn Library, 1990.

Glover, David. Sound and Light. New York: Kingfisher Books, 1993.

"Longitudinal and Transverse Wave Motion" (Web site). <http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html> (April 22, 2001).

"Multimedia Activities: Wave Motion." ExploreScience.com (Web site). <http://www.explorescience.com/activities/activity_list.cfm?categoryID=3> (April 22, 2001).

Ruchlis, Hyman. Bathtub Physics. Edited by Donald Barr; illustrated by Ray Skibinski. New York: Harcourt, Brace, and World, 1967.

"Wave Motion" (Web site). <http://www.media.uwe.ac.uk/masoud/projects/water/wave.html> (April 22, 2001).

"Wave Motion and Sound." The Physics Web (Web site). <http://www.hcrhs.hunterdon.k12.nj.us/disk2/Physics/wave.html> (April 22, 2001).

"Wave Motion Menu." Carson City-Crystal High School Physics and Chemistry Departments (Web site). <http://members.aol.com/cepeirce/b2.html> (April 22, 2001).