10 - Waves and Resonance 10 Of all the types of waves we...

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J. Newman, Physics of the Life Sciences , DOI: 10.1007/978-0-387-77259-2_10, © Springer Science+Business Media, LLC 2008 S IMPLE H ARMONIC M OTION R EVISITED: DAMPING AND R ESONANCE 249 Of all the types of waves we study, we are most familiar with water waves as seen in oceans, lakes, rivers, and bathtubs. We’re also familiar with waves created by air currents through fields of grasses or wheat. In reality, we constantly experience waves of various types. Sound, light, radio, and other forms of electromagnetic radiation surround us every moment of our lives and although we do not directly “see” their waves, aside from visible light, these phenomena can all be understood in terms of waves. Furthermore, we show later that matter also behaves as a wave and that our current quantum physics picture of the world is intimately connected with a mathematical description known as the wave func- tion. Waves are thus the key to our understanding of nature on a fundamental level. In this chapter we first return to the type of motion known as simple harmonic motion that we used to describe a mass on a spring in Chapter 3. Here we extend our previous dis- cussions to include the frictional loss of energy, known as damping, and the effects of a “driving force” used to sustain the motion. With the addition of energy by this external force comes the possibility of a resonance phenomenon in which the amplitude of oscil- lation can grow rapidly. This is an extremely important idea in physics that we will see often throughout the rest of our studies. We then introduce some fundamental concepts concerning waves and consider traveling waves along a string and along a coiled spring as mechanical examples of the two basic forms of waves, transverse and longitudinal. As waves travel along or through a medium, they meet and interact with boundaries or obsta- cles, and different interactions possible at a boundary are considered, including reflection and refraction. We also discuss one possible result from such boundary conditions, the cre- ation of standing waves. These are important in such diverse areas as musical instruments, the human ear, and the basic functioning of a laser, all considered later in this book. 1. SIMPLE HARMONIC MOTION REVISITED: DAMPING AND RESONANCE A linear restoring force is the basis of simple harmonic motion. Our example has been the spring force, F 52 kx , first studied in Chapter 3. The characteristic of sim- ple harmonic motion is the variation in oscillator position according to (10.1) where v 0 is the angular frequency that depends on the parameters of the particular type of simple harmonic oscillator. For example, in the case of a mass on a spring we have seen that the angular frequency is given by 0 5 . We have already introduced the definitions of the frequency, f , and period, T , which are related to the angular frequency in general by (10.2) f 0 5 1 T 5 v 0 2 p .
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10 - Waves and Resonance 10 Of all the types of waves we...

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