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CRC Press eBooks

Wave Motion

Carlos Calle

Published Dec 22, 2009• 0 citations
Publisher

Abstract

Wave motion exists everywhere. When a bird sings in the forest, sound waves propagate away from the bird’s throat in all directions, striking the ear membranes of the other animals nearby. A leaf falling from a tree on the surface of a pond produces ripples that spread outward through the surface of the serene water. Light reaching the surface of the earth from the sun propagates through empty space as an electromagnetic wave. And as we learned in Chapter 7, even ordinary matter exhibits wave behavior.

DOI
10.1201/9781439810743-25

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Wave motion exists everywhere. When a bird sings in the forest, sound waves propagate away from the bird’s throat in all directions, striking the ear membranes of the other animals nearby. A leaf falling from a tree on the surface of a pond produces ripples that spread outward through the surface of the serene water. Light reaching the surface of the earth from the sun propagates through empty space as an electromagnetic wave. And as we learned in Chapter 7, even ordinary matter exhibits wave behavior.
Waves of light Light behaves like a wave. In the laboratory, we can measure the vibrations that are set up in matter when a light wave comes by. We can also observe the peculiar light-and-dark patterns that occur when two light rays are made to act simultaneously, an unmistakable sign of wave behaviour. Let us make a small excursion into wave motion. Throughout this exposition, you are encouraged to experiment as much as possible with waves (preferably real ones, or at least those in the diagrams), to become familiar with their fascinating behaviour. Water waves in the bathtub, or those seen on open water from a high tower or an airplane, are especially instructive. Waves are periodic; if you pick a point in space (e.g. the surface of a pond at the point where a reed pokes through) and you watch the motion of the wave carrier (the water that bobs up and down), then you will see that the state of motion of the carrier repeats itself at regular intervals of time. This interval is the period of the wave. A free wave has a velocity, i.e. a direction and a speed. At a given point, a wave alternates periodically between a certain maximum and a minimum.
This chapter studies wave interference. Light does not bend in a lens, it does not bounce off the surface of glass, and it does not spread out after passing through a small hole. All of these are illusions. It only appears that light bends, bounces, and spreads out. The effects that people see—reflection, refraction, colors in soap bubbles—come from the fact that photons interact with one another in an unusual way. The interaction is often referred to as wave interference because it can be described mathematically much like the interference of water waves, but the reality of it is considerably stranger. The strangeness is discussed in more detail in the last chapter, but a hint of it can be seen from the fact that photons appear to interfere with one another even if they are emitted one at a time, which water waves obviously do not do.
Hands-on exercise: wave and particle properties The purpose of this exercise is for you to observe some basic wave and particle properties. To complete this exercise you will need the following: Tub of water, or access to a quiet pond, lake or swimming pool. Things to float on the surface of the water. Pen or pencil and some drawing paper. Small projectile such as a stone. Disturb the middle of the tub just until you are able to make a visible wave on the surface. Watch how the wave propagates. Wait until the surface of the water returns to being flat and make another wave. Keep doing this as many times as necessary to be able to draw what you see on the paper and answer the following questions: Does the wave have a definite location at any one moment in time? Does the wave have a definite direction as it propagates? Approximately how far does the wave travel in 1 s? Describe the motion of the water in which the wave moves. Throw your small projectile in the air at various angles, letting it drop down (not in the water). Keep doing this as many times as necessary to be able to draw what you see and answer the following questions: Does the object have a definite location at any one moment in time? […]
For all practical purposes the wave theory of light is a certainty. This is the story of a radical change in humans' concept of light. In 1896 most physicists were convinced that light consisted of wave disturbances in a medium, the electromagnetic aether. The energy transported in radiation was thought to propagate spherically outward from its source and to spread out over successively larger volumes in space. Thirty years later, a remarkably different concept of light prevailed. Physicists then took seriously the evidence collected over the preceding two decades showing that the energy of radiation does not spread in space. Under certain conditions, light behaves like a stream of particles. Our subject is more than the story of a shift from one theoretical explanation of radiation to another. This reconsideration of the nature of light was a significant event in our scientific understanding of the world. To resolve the paradox that faced them, physicists rejected the venerable Platonic dictum that the microscopic realm recapitulates the macroscopic; that laws generalized from the behavior of objects in the perceivable world may be applied to the imperceivable one. By 1927 physicists had assigned to all forms of radiation a curious amalgam of wave and particle behavior. Waves spread energy over larger and larger volumes of space; particles do not. Reconciliation of these conflicting properties was possible only through appeal to an ontology that transcended mechanical incompatibility. Nature was declared to be only imperfectly rationalizable in terms of human experience with macroscopic interactions. The programmatic goal formulated in the seventeenth century to reduce all physical phenomena to consistent mechanical representations was here recognized to be unattainable.
Light has long been perceived as a wave, or more specifically as an EM wave, and this is valid with respect to everyday observations. However, experiments involving light have produced surprising results that fall outside the realm of the wave nature of light. These experiments for the first time necessitated that light not be perceived as a wave but more like a particle. Some of these observations include photoelectric, Compton, and two-photon effects. In these experiments, light behaves more as an object filling a space just like a particle rather than a continuous entity like a wave. This is surprising given what we have learned in classical optics. In this chapter, we intend to analyze and understand the particle nature of light and its consequences.