Instructors_Guide_Ch20 - 20 Traveling Waves Recommended...

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20 Traveling Waves Recommended class days: 3 Background Information Waves are one of the two great models of classical physics, and wave phenomena appear through- out science and engineering. With waves, we move from the physics of particles to the physics of continuous media. Many of the ideas introduced during the study of waves will later be important for understanding electric fields and quantum-mechanical wave functions. In fact, my preference for treating thermodynamics before waves is because thermodynamics is a continuation of mechanics, whereas waves are more closely related to fields and wave functions. Student difficulties with wave motion have recently been studied (Wittman et al., 1999). In one question, students were shown a pulse traveling along a stretched string after flicking one end. Students were asked what could be done to cause the pulse to reach the wall sooner. The most common response was “Flick the string harder.” This and other questions have found that most students hold a particle-pulse model of wave propagation in which wave pulses travel through a medium as if they were particles. After all, the way to make a ball reach the wall sooner is to “Throw it harder.” The medium is seen merely as something that “the wave goes through,” like the ball going through the air, while the propagation speed depends on the initial conditions. This view of wave motion is incompatible with superposition, so it’s perhaps not surprising that few students could correctly sketch the waveform as two wave pulses passed through each other. These conceptual difficulties are compounded by the fact that waves are the first place students meet functions of two variables. Although this introduces mathematical complications, the more significant issue for most students is a difficulty visualizing what a wave looks like and how it moves through space. Textbook pictures are static images, and more often than not they show only one-dimensional, transverse waves. Students find it hard to imagine what the wave will look like at a later time or in a different position. Longitudinal waves and waves in two or three dimensions are even more difficult to visualize. Unfortunately, it’s difficult to demonstrate traveling waves in the classroom. Nearly all demonstrations reflect at the end to set up standing waves. Consequently, this is one area where commercially available videos and computer simulations can be especially helpful. Computer simulations are especially good for showing how the motion of the wave differs from the motion of particles in the medium. Wave fronts and wave front diagrams are another source of difficulty, likely because pictures show them at only a single instant of time. As a result, some students end up thinking that the wave fronts are fixed at certain points in space. Other students don’t understand how wave fronts are related to a graph of a wave. Because all students are familiar with ripples moving out from the
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Instructors_Guide_Ch20 - 20 Traveling Waves Recommended...

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