CONCEPT
When two or more waves interact and combine, they interfere with one another. But interference is not necessarily bad: waves may interfere constructively, resulting in a wave larger than the original waves. Or, they may interfere destructively, combining in such a way that they form a wave smaller than the original ones. Even so, destructive interference may have positive effects: without the application of destructive interference to the muffler on an automobile exhaust system, for instance, noise pollution from cars would be far worse than it is. Other examples of interference, both constructive and destructive, can be found wherever there are waves: in water, in sound, in light.
HOW IT WORKS
Waves
Whenever energy ripples through space, there is a wave. In fact, wave motion can be defined as a type of harmonic motion (repeated movement of a particle about a position of equilibrium, or balance) that carries energy from one place to another without actually moving any matter. A wave on the ocean is an example of a mechanical wave, or one that involves matter; but though the matter moves in place, it is only the energy in the wave that experiences net movement.
Wave motion is related to oscillation, a type of harmonic motion in one or more dimensions. There is one critical difference, however: oscillation involves no net movement, only movement in place, whereas the harmonic motion of waves carries energy from one place to another. Yet, individual waves themselves are oscillating even as the overall wave pattern moves.
A transverse wave forms a regular up-and-down pattern in which the oscillation is perpendicular to the direction the wave is moving. Ocean waves are transverse, though they also have properties of longitudinal waves. In a longitudinal wave, of which a sound wave is the best example, oscillation occurs in the same direction as the wave itself.
Parameters of wave Motion
Some waves, composed of pulses, do not follow regular patterns. However, the waves of principal concern in the present context are periodic waves, ones in which a uniform series of crests and troughs follow each other in regular succession. Periodic motion is movement repeated at regular intervals called periods. In the case of wave motion, a period (represented by the symbol T) is the amount of time required to complete one full cycle of the wave, from trough to crest and back to trough.
Period can be mathematically related to several other aspects of wave motion, including wave speed, frequency, and wavelength. 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; 103 or 1,000 cycles per second) or megahertz (MHz; 106 or 1 million cycles per second.) Wavelength (represented by the symbol abbreviated X, the Greek letter lambda) is the distance between a crest and the adjacent crest, or a
A piano tuner, using a tuning fork such as the ones shown above, utilizes interference to tune the instrument.
trough and an adjacent trough, of a wave. The higher the frequency, the shorter the wavelength.
Another parameter for describing wave motion—one that is mathematically independent from the quantities so far described—is amplitude, or the maximum displacement of particles from a position of stable equilibrium. For an ocean wave, amplitude is the distance from either the crest or the trough to the level that the ocean would maintain if it were perfectly still.
Superposition and Interference
superposition. The principle of superposition holds that when several individual but similar physical events occur in close proximity, the resulting effect is the sum of the magnitude of the separate events. This is akin to the popular expression, “The whole is greater than the sum of the parts,” and it has numerous applications in physics.
Where the strength of a gravitational field is being measured, for instance, superposition dictates that the strength of that field at any given point is the sum of the mass of the individual particles in that field. In the realm of electromagnetic force, the same statement applies, though the units being added are electrical charges or magnetic poles, rather than quantities of mass. Likewise, in an electrical circuit, the total current or voltage is the sum of the individual currents and voltages in that circuit.
Superposition applies only in equations for linear events—that is, phenomena that involve movement along a straight line. Waves are linear phenomena, and, thus, the principle describes the behavior of all waves when they come into contact with one another. If two or more waves enter the same region of space at the same time, then, at any instant, the total disturbance produced by the waves at any point is equal to the sum of the disturbances produced by the individual waves.
Interference
The principle of superposition does not require that waves actually combine; rather, the net effect is as though they were combined. The actual combination or joining of two or more waves at a given point in space is called interference, and, as a result, the waves produce a single wave whose properties are determined by the properties of the individual waves.
If two waves of the same wavelength occupy the same space in such a way that their crests and
If this boat’s wake were to cross the wake of another boat, the result would be both constructive and destructive interference.
troughs align, the wave they produce will have an amplitude greater than that possessed by either wave initially. This is known as constructive interference. The more closely the waves are in phase—that is, perfectly aligned—the more constructive the interference.
It is also possible that two or more waves can come together such that the trough of one meets the crest of the other, or vice versa. In this case, what happens is destructive interference, and the resulting amplitude is the difference between the values for the individual waves. If the waves are perfectly unaligned—in other words, if the trough of one exactly meets the crest of the other—their amplitudes cancel out, and the result is no wave at all.
Resonance
It is easy to confuse interference with resonance, and, therefore, a word should be said about the latter phenomenon. The term resonance describes a situation in which force is applied to an oscillator at the point of maximum amplitude. In this way, the motion of the outside force is perfectly matched to that of the oscillator, making possible a transfer of energy. As with interference, resonance implies alignment between two physical entities; however, there are several important differences.
Resonance can involve waves, as, for instance, when sound waves resonate with the vibrations of an oscillator, causing a transfer of energy that sometimes produces dramatic results. (See essay on Resonance.) But in these cases, a wave is interacting with an oscillator, not a wave with a wave, as in situations of interference. Furthermore, whereas resonance entails a transfer of energy, interference involves a combination of energy.
Transfer vs. Combination
The importance of this distinction is easy to see if one substitutes money for energy, and people for objects. If one passes on a sum of money to another person, a business, or an institution—as a loan, repayment of a loan, a purchase, or a gift—this is an example of a transfer. On the other hand, when married spouses each earn paychecks, their cash is combined.
Transfer thus indicates that the original holder of the cash (or energy) no longer has it. Yet, if the holder of the cash combines funds with those of another, both share rights to an amount of money greater than the amount each originally owned. This is analogous to constructive interference.
On the other hand, a husband and wife (or any other group of people who pool their cash) also share liabilities, and, thus, a married person may be subject to debt incurred by his or her spouse. If one spouse creates debt so great that the other spouse cannot earn enough to maintain the payments, this painful situation is analogous to destructive interference.
REAL-LIFE APPLICATIONS
Mechanical Waves
One of the easiest ways to observe interference is by watching the behavior of mechanical waves. Drop a stone into a still pond, and watch how its waves ripple: this, as with most waveforms in water, is an example of a surface wave, or one that displays aspects of both transverse and longitudinal wave motion. Thus, as the concentric circles of a longitudinal wave ripple outward in one dimension, there are also transverse movements along a plane perpendicular to that of the longitudinal wave.
While the first wave is still rippling across the water, drop another stone close to the place where the first one was dropped. Now, there are two surface waves, crests and troughs colliding and interfering. In some places, they will interfere constructively, producing a wave—or rather, a portion of a wave—that is greater in amplitude than either of the original waves. At other places, there will be destructive interference, with some waves so perfectly out of phase that at one instant in time, a given spot on the water may look as though it had not been disturbed at all.
One of the interesting aspects of this interaction is the lack of uniformity in the instances of interference. As suggested in the preceding paragraph, it is usually not entire waves, but merely portions of waves, that interfere constructively or destructively. The result is that a seemingly simple event—dropping two stones into a still pond—produces a dazzling array of colliding circles, broken by outwardly undisturbed areas of destructive interference.
A similar phenomenon, though manifested by the interaction of geometric lines rather than concentric circles, occurs when two power boats pass each other on a lake. The first boat chops up the water, creating a wake that widens behind it: when seen from the air, the boat appears to be at the apex of a triangle whose sides are formed by rippling eddies of water.
Now, another boat passes through the wake of the first, only it is going in the opposite direction and producing its own ever-widening wake as it goes. As the waves from the two boats meet, some are in phase, but, more often than not, they are only partly in phase, or they possess differing wavelengths. Therefore, the waves at least partially cancel out one another in places, and in other places, reinforce one another. The result is an interesting patchwork of patterns when seen from the air.
Sound Waves in tune and out of tune
The relationships between musical notes can be intriguing, and though tastes in music vary, most people know when music is harmonious and when it is discordant. As discussed in the essay on frequency, this harmony or discord can be equated to the mathematical relationships between the frequencies of specific notes: the lower the numbers involved in the ratio, the more pleasing the sound.
The ratio between the frequency of middle C and that of its first harmonic—that is, the C note exactly one octave above it—is a nice, clean 1:2. If one were to play a song in the key of C-which, on a piano, involves only the “white notes” C-D-E-F-G-A-B—everything should be perfectly harmonious and (presumably) pleasant to the ear. But what if the piano itself is out of tune? Or what if one key is out of tune with the others?
The result, for anyone who is not tone-deaf, produces an overall impression of unpleasantness: it might be a bit hard to identify the source of this discomfort, but it is clear that something is amiss. At best, an out-of-tune piano might sound like something that belonged in a saloon from an old Western; at worst, the sound of notes that do not match their accustomed frequencies can be positively grating.
How a tuning fork works
To rectify the situation, a professional piano tuner uses a tuning fork, an instrument that produces a single frequency—say, 264 Hz, which is the frequency of middle C. The piano tuner strikes the tuning fork, and at the same time strikes the appropriate key on the piano. If their frequencies are perfectly aligned, so is the sound of both; but, more likely, there will be interference, both constructive and destructive.
As time passes—measured in seconds or even fractions of seconds—the sounds of the tuning fork and that of the piano key will alternate between constructive and destructive interference. In the case of constructive interference, their combined sound will become louder than the individual sounds of either; and when the interference is destructive, the sound of both together will be softer than that produced by either the fork or the key.
The piano tuner listens for these fluctuations of loudness, which are called beats, and adjusts the tension in the appropriate piano string until the beats disappear completely. As long as there are beats, the piano string and the tuning fork will produce together a frequency that is the average of the two: if, for instance, the out-of-tune middle C string vibrates at 262 Hz, the resulting frequency will be 263 Hz.
Difference Tones
Another interesting aspect of the interaction between notes is the “difference tone,” created by discord, which the human ear perceives as a third tone. Though E and F are both part of the C scale, when struck together, the sound is highly discordant. In light of what was said above about ratios between frequencies, this dissonance is fitting, as the ratio here involves relatively high numbers—15:16.
When two notes are struck together, they produce a combination tone, perceived by the human ear as a third tone. If the two notes are harmonious, the “third tone” is known as a summation tone, and is equal to the combined frequencies of the two notes. But if the combination is dissonant, as in the case of E and F, the third tone is known as a difference tone, equal to the difference in frequencies. Since an E note vibrates at 330 Hz, and an F note at 352 Hz, the resulting difference tone is equal to 22 Hz.
DESTRUCTIVE INTERFERENCE IN SOUND WAVES
When music is played in a concert hall, it reverberates off the walls of the auditorium. Assuming the place is well designed acoustically, these bouncing sound waves will interfere constructively, and the auditorium comes alive with the sound of the music. In other situations, however, the sound waves may interfere destructively, and the result is a certain muffled deadness to the sound.
Clearly, in a music hall, destructive interference is a problem; but there are cases in which it can be a benefit—situations, that is, in which the purpose, indeed, is to deaden the sound. One example is an automobile muffler. A car’s exhaust system makes a great deal of noise, and, thus, if a car does not have a proper muffler, it creates a great deal of noise pollution. A muffler counteracts this by producing a sound wave out of phase with that of the exhaust system; hence, it cancels out most of the noise.
Destructive interference can also be used to reduce sound in a room. Once again, a machine is calibrated to generate sound waves that are perfectly out of phase with the offending noise— say, the hum of another machine. The resulting effect conveys the impression that there is no noise in the room, though, in fact, the sound waves are still there; they have merely canceled each other out.
Electromagnetic Waves
In 1801, English physicist Thomas Young (17731829), known for Young’s modulus of elasticity became the first scientist to identify interference in light waves. Challenging the corpuscular theory of light put forward by Sir Isaac Newton (1642-1727), Young set up an experiment in which a beam of light passed through two closely spaced pinholes onto a screen. If light was truly made of particles, he said, the beams would project two distinct points onto the screen. Instead, what he saw was a pattern of interference.
In fact, Newton was partly right, but Young’s discovery helped advance the view of light as a wave, which is also partly right. (According to quantum theory, developed in the twentieth century, light behaves both as waves and as particles.) The interference in the visible spectrum that Young witnessed was manifested as bright and dark bands. These bands are known as fringes—variations in intensity not unlike the beats created in some instances of sound interference, described above.
OILY FILMS AND RAINBOWS
Many people have noticed the strangely beautiful pattern of colors generated when light interacts with an oily substance, as when light reflected on a soap bubble produces an astonishing array of shades. Sometimes, this can happen in situations not otherwise aesthetically pleasing: an oily film in a parking lot, left there by a car’s leaky crankcase, can produce a rainbow of colors if the sunlight hits it just right.
KEY TERMS
Amplitude: The maximum displacement of particles in oscillation from a position of stable equilibrium. For an ocean wave, amplitude is the distance from either the crest or the trough to the level that the ocean would maintain if it were perfectly still.
Constructive interference:A type of interference that occurs when two or more waves combine in such a way that they produce a wave whose amplitude is greater than that of the original waves. If waves are perfectly in phase—in other words, if the crest and trough of one exactly meets the crest and trough of the other—then the resulting amplitude is the sum of the individual amplitudes of the separate waves.
Cycle: In oscillation, a cycle occurs when the oscillating particle moves from a certain point in a certain direction, then switches direction and moves back to the original point. Typically, this is from the position of stable equilibrium to maximum displacement and back again to the stable equilibrium position. In a wave, a cycle is equivalent to the movement from trough to crest and back to trough.
Destructive interference: A type of interference that occurs when two or more waves combine to produce a wave whose amplitude is less than that of the original waves. If waves are perfectly out of phase—in other words, if the trough of one exactly meets the crest of the other, and vice versa—their amplitudes cancel out, and the result is no wave at all.
Frequency: In wave motion, frequency is the number of waves passing through a given point during the interval of one second. The higher the frequency, the shorter the wavelength. Frequency is mathematically related to wave speed and period.
Harmonic motion: The repeated movement of a particle about a position of equilibrium, or balance.
Hertz: A unit for measuring frequency, named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894). High frequencies are expressed in terms of kilohertz (kHz; 103 or 1,000 cycles per second) or megahertz (MHz; 106 or 1 million cycles per second.)
Interference: The combination of two or more waves at a given point in space to produce a wave whose properties are determined by the properties of the individual waves. This accords with the principle of superposition.
Longitudinal wave: A wave in which the movement of vibration is in the same direction as the wave itself. This is contrasted to a transverse wave.
Maximum displacement: For an object in oscillation, maximum displacement is the furthest point from stable equilibrium.
Mechanical wave: A type of wave—for example, a wave on the ocean— that involves matter. The matter itself may move in place, but as with all types of wave motion, there is no net movement of matter—only of energy.
Oscillation: A type of harmonic motion, typically periodic, in one or more dimensions.
Period: For wave motion, a period is the amount of time required to complete one full cycle. Period is mathematically related to frequency, wavelength, and wave speed.
Periodic motion: Motion that is repeated at regular intervals. These intervals are known as periods. periodic wave: A wave in which a uniform series of crests and troughs follow one after the other in regular succession. phase: When two waves of the same frequency and amplitude are perfectly aligned, they are said to be in phase.
Principle of superposition:
A physical principle stating that when several individual, but similar, physical events occur in close proximity to one another, the resulting effect is the sum of the magnitude of the separate events. Interference is an example of superposition. pulse: An isolated, non-periodic disturbance that takes place in wave motion of a type other than that of a periodic wave. resonance: The condition in which force is applied to an object in oscillation at the point of maximum amplitude.
Stable equilibrium: A position in which, if an object were disturbed, it would tend to return to its original position. For an object in oscillation, stable equilibrium is in the middle of a cycle, between two points of maximum displacement.
Surface wave: A wave that exhibits the behavior of both a transverse wave and a longitudinal wave.
Transverse wave: A wave in which the vibration or motion is perpendicular to the direction in which the wave is moving. This is contrasted to a longitudinal wave.
Wavelength: The distance between a crest and the adjacent crest, or the trough and an adjacent trough, of a wave. Wavelength, abbreviated X (the Greek letter lambda) is mathematically related to wave speed, period, and frequency.
Wave motion: A type of harmonic motion that carries energy from one place to another, without actually moving any matter.
This happens because the thickness of the oil causes a delay in reflection of the light beam. Some colors pass through the film, becoming delayed and, thus, getting out of phase with the reflected light on the surface of the film. These shades destructively interfere to such an extent that the waves are cancelled, rendering them invisible. Other colors reflect off the surface so that they are perfectly in phase with the light traveling through the film, and appear as an attractive swirl of color on the surface of the oil.
The phenomenon of light-wave interference with oily or filmy surfaces has the effect of filtering light, and, thus, has a number of applications in areas relating to optics: sunglasses, lenses for binoculars or cameras, and even visors for astronauts. In each case, unfiltered light could be harmful or, at least, inconvenient for the user, and the destructive interference eliminates certain colors and unwanted reflections.
Radio waves
Visible light is only a small part of the electromagnetic spectrum, whose broad range of wave phenomena are, likewise, subject to constructive or destructive interference. After visible light, the area of the spectrum most people experience during an average day is the realm of relatively low-frequency, long-wavelength radio waves and microwaves, the latter including television broadcast signals.
People who rely on an antenna for their TV reception are likely to experience interference at some point. However, an increasing number of Americans use either cable or satellite systems to pick up TV programs. These are much less susceptible to interference, due to the technology of coaxial cable, on the one hand, and digital compression, on the other. Thus, interference in television reception is a gradually diminishing problem.
Interference among radio signals continues to be a challenge, since most people still hear the radio via old-fashioned means rather than through new technology, such as the Internet. A number of interference problems are created by activity on the Sun, which has an enormously powerful electromagnetic field. Obviously, such interference is beyond the control of most radio listeners, but according to a Web page set up by WHKY Radio in Hickory, North Carolina, there are a number of things listeners can do to decrease interference in their own households.
Among the suggestions offered at the WHKY Web site is this: “Nine times out of ten, if your radio is near a computer, it will interfere with your radio. Computers send out all kinds of signals that your radio ‘thinks’ is a real radio signal. Try to locate your radio away from computers… especially the monitor.” The Web site listed a number of other household appliances, as well as outside phenomena such as power lines or thunderstorms, that can contribute to radio interference.
