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Traveling Waves

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Book Id: WPLBN0000686535
Format Type: PDF eBook
File Size: 301.06 KB.
Reproduction Date: 2005

Title: Traveling Waves  
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Language: English
Subject: Science., Physics, Physics--Research
Collections: Physics Literature
Historic
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Traveling Waves. (n.d.). Traveling Waves. Retrieved from http://hawaiilibrary.net/


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Physics Literature

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Introduction: The standing waves we found as solutions to the wave equation can be used to explain any type of vibration in continuous media, since they represent the most general solution to the problem. Any arbitrary set of initial conditions can be taken care of by appropriately selecting the adjustable parameters in the expression for the standing waves. On the other hand, these standing waves are particularly inappropriate to illustrate certain kind of very common wave phenomena. Suppose for example that you drop a stone on the surface of a lake. You see a circular wave traveling away from the point where the stone hits the water. This appears to be a very simple (and beautiful) type of motion, yet it is by no means clear how this simplicity shows up when we write the disturbance as some type of combination of standing waves in the lake. You had a similar experience when you solved Problem 2 in Chapter 5. After a very complicated series expansion, your final solution is so simple that it can be accurately described in words: the initial perturbation splits into two equally shaped pulses that travel without distortion toward the ends of the cord. The simplicity of the traveling waves is such that even football fans - not necessarily the most (mathematically) gifted members of our society - have no trouble generating waves that travel back and forth around the stadium. In this chapter, we will show that the solutions to the wave equation can indeed be written as traveling waves. Traveling waves are not new, additional solutions to the wave equation. Rather, the standing wave solutions can be written as traveling waves. In many practical cases, the traveling wave form turns out to be much simpler than the standing wave form.

 

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