4.1 Give us a Wave

 

If we are going to pursue our idea from chapter 1, that particles of matter behave, in some ways at least, like waves, we need to ask one key question:  what’s a wave?  In this chapter we’ll explore that idea in general, and learn how to describe a wave mathematically.

In general a wave is an oscillation in one dimension (ie something that varies in a repetitive way as a function of time) which extends out in other dimensions. In the case of a travelling wave, the oscillation propagates outwards, so that the maximum and minimum of the oscillation move in space as time progresses (stationary waves are also possible, as we saw in chapter 1 – more about these later). 

In the case of an ocean wave, for example, the molecules in the water move only vertically, up and down, but the maxima and minima in the resulting wave move horizontally across the ocean surface. In an electromagnetic wave, such as light, perpendicular electric and magnetic fields oscillate in a similar way, the maxima and minima in these fields propagating through space.

As we shall see, waves don’t all have the same shape, but the most familiar wave form, and the key building block for constructing more complex forms, is a sine wave, so that’s where we’ll start.