16 - Wave Motion

16 wave motion

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Unformatted text preview: PUZZLER A simple seismograph can be constructed with a spring-suspended pen that draws a line on a slowly unrolling strip of paper. The paper is mounted on a structure attached to the ground. During an earthquake, the pen remains nearly stationary while the paper shakes beneath it. How can a few jagged lines on a piece of paper allow scientists at a seismograph station to determine the distance to the origin of an earthquake? (Ken M. Johns/Photo Researchers, Inc.) chapter Wave Motion Chapter Outline 16.1 Basic Variables of Wave Motion 16.2 Direction of Particle Displacement 16.3 One-Dimensional Traveling Waves 16.4 Superposition and Interference 16.5 The Speed of Waves on Strings 490 16.6 Reflection and Transmission 16.7 Sinusoidal Waves 16.8 Rate of Energy Transfer by Sinusoidal Waves on Strings 16.9 (Optional) The Linear Wave Equation 16.1 Wave Motion M ost of us experienced waves as children when we dropped a pebble into a pond. At the point where the pebble hits the water’s surface, waves are created. These waves move outward from the creation point in expanding circles until they reach the shore. If you were to examine carefully the motion of a leaf floating on the disturbed water, you would see that the leaf moves up, down, and sideways about its original position but does not undergo any net displacement away from or toward the point where the pebble hit the water. The water molecules just beneath the leaf, as well as all the other water molecules on the pond’s surface, behave in the same way. That is, the water wave moves from the point of origin to the shore, but the water is not carried with it. An excerpt from a book by Einstein and Infeld gives the following remarks concerning wave phenomena:1 A bit of gossip starting in Washington reaches New York [by word of mouth] very quickly, even though not a single individual who takes part in spreading it travels between these two cities. There are two quite different motions involved, that of the rumor, Washington to New York, and that of the persons who spread the rumor. The wind, passing over a field of grain, sets up a wave which spreads out across the whole field. Here again we must distinguish between the motion of the wave and the motion of the separate plants, which undergo only small oscillations... The particles constituting the medium perform only small vibrations, but the whole motion is that of a progressive wave. The essentially new thing here is that for the first time we consider the motion of something which is not matter, but energy propagated through matter. The world is full of waves, the two main types being mechanical waves and electromagnetic waves. We have already mentioned examples of mechanical waves: sound waves, water waves, and “grain waves.” In each case, some physical medium is being disturbed — in our three particular examples, air molecules, water molecules, and stalks of grain. Electromagnetic waves do not require a medium to propagate; some examples of electromagnetic waves are visible light, radio waves, television signals, and x-rays. Here, in Part 2 of this book, we study only mechanical waves. The wave concept is abstract. When we observe what we call a water wave, what we see is a rearrangement of the water’s surface. Without the water, there would be no wave. A wave traveling on a string would not exist without the string. Sound waves could not travel through air if there were no air molecules. With mechanical waves, what we interpret as a wave corresponds to the propagation of a disturbance through a medium. Interference patterns produced by outwardspreading waves from many drops of liquid falling into a body of water. 1 A. Einstein and L. Infeld, The Evolution of Physics, New York, Simon & Schuster, 1961. Excerpt from “What Is a Wave?” 491 492 CHAPTER 16 Wave Motion The mechanical waves discussed in this chapter require (1) some source of disturbance, (2) a medium that can be disturbed, and (3) some physical connection through which adjacent portions of the medium can influence each other. We shall find that all waves carry energy. The amount of energy transmitted through a medium and the mechanism responsible for that transport of energy differ from case to case. For instance, the power of ocean waves during a storm is much greater than the power of sound waves generated by a single human voice. 16.1 y λ x λ Figure 16.1 The wavelength of a wave is the distance between adjacent crests, adjacent troughs, or any other comparable adjacent identical points. BASIC VARIABLES OF WAVE MOTION Imagine you are floating on a raft in a large lake. You slowly bob up and down as waves move past you. As you look out over the lake, you may be able to see the individual waves approaching. The point at which the displacement of the water from its normal level is highest is called the crest of the wave. The distance from one crest to the next is called the wavelength (Greek letter lambda). More generally, the wavelength is the minimum distance between any two identical points (such as the crests) on adjace...
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This note was uploaded on 03/24/2010 for the course PHYSICS 2202 taught by Professor Mihalisin during the Spring '09 term at Temple.

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