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Introduction to Waves

16.1-16.3 and 16.7-16.8

We are not doing all of this chapter and we will not do too much with pulse type waves. We will mostly concentrate on the sinusoidal wave of section 16.3. Section 16.7 extends the discussion to 2 and 3D while 16.8 discusses energy and intensity of a wave.

Section 16.4 derives the wave equation. This is a very important differential equation in physics and it will be re-derived next week for the electromagnetic wave but the math is beyond the level of this course. It is worth it to have a look though.

Chap 16 is a general treatment of any wave. We will focus on the E&M wave which is a transverse wave.

In the video below, Prof. Leblond alludes to the E&M wave which we will see next week.

There are many different type of waves: sound, waves in water, pulse on a string, light, and many more. The basic definition of a wave is “It is a disturbance from equilibrium that propagates with time from one region of space to another."

In the slow motion movie below we see water which is made of a very large number of atoms. When a droplet falls on the surface it creates a disturbance which propagates away from where the droplet fell. That is the wave. If you have a single droplet falling, we get a single non-repeating disturbance. We call that a pulse. If your faucet was leaking a droplet every second, we would get a periodic repeating wave in the water.

Oscillations vs Waves

A wave varies in space with wavelength \lambda . A plot of a wave variation in space looks like

The wavelength is the distance between peaks. Note that position, x, not the time, is on the horizontal axis. This is important not to confuse this figure ("Graphical Representation of Wave") with the oscillation graph ("Graph of an Oscillatory Motion").

This is super important, a wave has two oscillations, in time and in space. The book use the wording of the snapshot graph (oscillate in space at a given time) and a history graph (at a point in space, what happened over time). When you look at a wave graph, take note on the horizontal axis to make sure you know which one is which.
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