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Chapter 14 Vibrations and Waves

To most people, waves conjure up images of water waves striking a lake shore or an oceanfront. When you throw a stone in water you can clearly see the circular water waves traveling outward from the point of impact (Figure 14.0.1). There are many types of waves in nature, e.g. sound waves, seismic waves, waves on a string, electromagnetic waves, etc., just to a name a few of the commonly encountered ones.

Figure 14.0.1. Waves in lake generated by dropping a stone.

There is a close connection between waves and vibration. Waves get generated by something vibrating at the source. In the case of sound, the wave travels through a medium, such as air, by vibrating the particles of the medium.

Waves transport energy and momentum over space without an actual transport of material. When a sound wave travels through air, the air particles oscillate to and fro about their equilibrium point in the direction of the wave. The oscillating particles of air are coupled to each other so that oscillation of one layer of particles can lead to the oscillation of the neighboring particles, thereby transferring energy to their neighbors. The mechanism does not require the transport of air particles themselves, but just the transfer of energy and momentum of the particles through local oscillations. The pattern of oscillations make up a wave.

In this chapter we will study common characteristics of all waves using mainly the mechanical waves on a taut string as an example. I have made this choice to keep both math and pictures simpler. For instance, Figure 14.0.2 shows how shaking a string up and down sinusoidally leads to generation of wae down the string.

Figure 14.0.2. Waves in lake generated by dropping a stone.