Lesson 1: The Nature of a Wave

Waves and wavelike Motion

Waves are everywhere. Whether we recognize or not, we encounter waves on a daily basis. Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, cosine waves, telephone chord waves, stadium waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of our daily encounters with waves. In addition to waves, there are a variety of phenomenon in our physical world which resemble waves so closely that we can describe such phenomenon as being wavelike. The motion of a pendulum, the motion of a mass suspended by a spring, the motion of a child on a swing, and the "Hello, Good Morning!" wave of the hand can be thought of as wavelike phenomena. Waves (and wavelike phenomena) are everywhere!

We study the physics of waves because it provides a rich glimpse into the physical world which we seek to understand and describe as physicists. Before beginning a formal discussion of the nature of waves, it is often useful to ponder the various encounters and exposures which we have of waves. Where do we see waves or examples of wavelike motion? What experiences do we already have which will help us in understanding the physics of waves?

For many people, the first thought concerning waves conjures up a picture of a wave moving across the surface of an ocean, lake,pond or other body of water. The waves are created by some form of a disturbance, such as a rock thrown into the water, a duck shaking its tail in the water or a boat moving through the water. The water wave has a crest and a trough and travels from one location to another. One crest is often followed by a second crest which is often followed by a third crest. Every crest is separated by a trough to create an alternating pattern of crests and troughs. A duck or gull at rest on the surface of the water is observed to bob up-and-down at rather regular time intervals as the wave passes by. The waves may appear to be plane waves which travel together as a front in a straight-line direction, perhaps towards a sandy shore. Or the waves may be circular waves which originate from the point where the disturbances occur; such circular waves travel across the surface of the water in all directions. These mental pictures of water waves are useful for understanding the nature of a wave and will be revisited later when we begin our formal discussion of the topic.

The thought of waves often brings to mind a recent encounter at the baseball or football stadium when the crowd enthusiastically engaged in "doing the wave." When performed with reasonably good timing, a noticeable ripple is produced which travels around the circular stadium or back and forth across a section of bleachers. The observable ripple results when a group of enthusiastic fans rise up from their seats, swing their arms up high, and then sit back down. Beginning in Section 1, the first row of fans abruptly rise up to begin the wave; as they sit back down, row 2 begins its motion; as row 2 sits back down, row 3 begins its motion. The process continues, as each consecutive row becomes involved by a momentary standing up and sitting back down. The wave is passed from row to row as each individual member of the row becomes temporarily displaced out of their seat, only to return to it as the wave passes by. This mental picture of a stadium wave will also provide a useful context for the discussion of the physics of wave motion.

Another picture of waves involves the movement of a slinky or similar set of coils. If a slinky is stretched out from end to end, a wave can be introduced into the slinky by either vibrating the first coil up and down vertically or back and forth horizontally. A wave will subsequently be seen traveling from one end of the slinky to the other. As the wave moves along the slinky, each individual coil is seen to move out of place and then return to its original position. The coils always move in the same direction that the first coil was vibrated. A continued vibration of the first coil results in a continued back and forth motion of the other coils. If looked at closely, one notices that the wave does not stop when it reaches the end of the slinky; rather it seems to bounce off the end and head back from where it started. A slinky wave provides an excellent mental picture of a wave and will be use in discussions and demonstrations throughout this unit.

Telephone chord waves provide another mental picture of waves. A telephone chord wave is created when a contented teenager stretches out the chord and unconsciously vibrates one end of the chord. A disturbance is created which subsequently moves along the chord, reaches the wall and returns to the hand set. A single disturbance can be created by the single vibration of one end of the chord or a repeated disturbance can be created by the repeated and regular vibration of the end of the chord. If one ever consciously awakes and observes the motion of the telephone chord, they soon become aware of a wealth of physics. The shape of the chord is actually influenced by the frequency at which it is vibrated. If the student vibrates the chord rather frequently, then a short wave is created; and if the student vibrates the chord at a low frequency (not so often), then a long wave is created.

Then there is the "Hello, Good Morning!" wave. Whether encountered in the driveway as you begin your trip to school, on the street on the way to school, in the parking lot upon arrival to school, or in the hallway on the way to your first class, the "Hello, Good Morning!" wave provides a simple (yet excellent) example of physics in action. The simple back and forth motion of the hand is called a "wave." When Mom commands us to "wave to Mr. Smith," she is telling us to raise our hand and to temporarily or even repeatedly vibrate it back and forth. The hand is raised, moved to the left, then back to the far right and finally returns to its original position. Energy is put into the hand and the hand begins its back-and-forth vibrational motion. And we call the process of doing it "waving." Soon we will see how this simple act is representative of the nature of a physical wave.

We also encountered waves in Math class in the form of the sine and cosine function. We often plotted y=Bsine(Ax) on our calculator or by hand and observed that its graphical shape resembled the characteristic shape of a wave. There was a crest and a trough and a repeating pattern. If we changed the constant A in the equation, we noticed that we could change the length of the wave. And if we changed B in the equation, we noticed that we changed the height of the wave. In math class, we encountered the underlying mathematical functions which describe the physical nature of waves.

Finally, we are familiar with microwaves and visible light waves. While we have never seen them, we believe that they exist because we have witnessed how they carry energy from one location to another. And similarly, we are familiar with radio waves and sound waves. Like microwaves, we have never seen them. Yet we believe they exist because we have witnessed the signals which they carry from one location to another and we have even learned how to tune into those signals through use of our ears or a tuner on a television or radio. Waves, as we will learn, carry energy from one location to another. And if the frequency of those waves can be changed, then we can also carry a complex signal which is capable of transmitting an idea or thought from one location to another. Perhaps this is one of the most important aspects of waves and will become a focus of our study in later units.

Waves are everywhere in nature. Our understanding of the physical world is not complete until we understand the nature, properties and behaviors of waves. The goal of this unit is to develop mental models of waves and ultimately apply those models to an understanding of the two most common types of waves - sound waves and light waves.

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