16 - Wave Motion - PUZZLER A simple seismograph can be...

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c h a p t e r Wave Motion P U Z Z L E R A simple seismograph can be con- structed 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 be- neath it. How can a few jagged lines on a piece of paper allow scientists at a seis- mograph station to determine the dis- tance to the origin of an earthquake? (Ken M. Johns/Photo Researchers, Inc.) C h a p t e r O u t l i n e 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 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 P U Z Z L E R 490
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16.1 Wave Motion 491 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 cre- ated. These waves move outward from the creation point in expanding cir- cles 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 displace- ment 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 in- volved, 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 be- tween the motion of the wave and the motion of the separate plants, which un- dergo 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 elec- tromagnetic 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 mole- cules, and stalks of grain. Electromagnetic waves do not require a medium to propa-
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