# 8: Traveling Waves

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In this chapter, we show how the same physics that leads to standing wave oscillations also gives rise to waves that move in space as well as time. We then go on to introduce the important physical example of light waves.

## Preview

In an infinite translation invariant system, traveling waves arise naturally from the complex exponential behavior of the solutions in space and time.

1. We begin by showing the connection between standing waves and traveling waves in infinite systems. A traveling wave in a linear system is a pair of standing waves put together with a special phase relation. We show how traveling waves can be produced in finite systems by appropriate forced oscillations.
2. We then go on to discuss the force and power required to produce a traveling wave on a string, and introduce the useful idea of “impedance.”
3. We introduce and discuss the most important classical example of wave phenomena, electromagnetic waves and light.
4. We reexamine the translation invariant systems of coupled $$LC$$ circuits discussed in chapter 5 and show how they are related to electromagnetic waves.
5. We discuss the effects of damping in translation invariant systems, giving a simple physical interpretation of the effect of traveling waves.
6. We discuss traveling waves in systems with damping and in systems with high and/or low frequency cut-offs.

This page titled 8: Traveling Waves is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Howard Georgi via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.