Waves and wave motion

We have been investigating for the past few classes the phenomenon of simple harmonic motion, in which an object simply moves up and down, or back and forth, around some equilibrium position.

Image and video courtesy of Rhett Allen

We have seen that the position of the object can be described by a sine or cosine function of time.

This mathematical equation is very similar to that which can be used to describe the shape of a guitar string which has been plucked:

Image and video courtesy of Brotheroff

If we just turn this picture on its side, and add the standard axes,

then we can describe the shape of a guitar string, frozen in this photograph, with an equation like this:

But in real life, we often encounter situations in which material is oscillating both BOTH time AND space -- at the same time!

Image and video courtesy of National STEM Centre

We call these phenomena WAVES. In order to describe waves mathematically, we will need to mix time (t) and space (x) together -- sort of like chocolate and peanut butter.

What are waves? They can be described briefly as disturbances in a medium which transfer energy and information from point A to point B.^* The key fact is that no physical object actually travels from point A to point B --- and yet both energy and information make the trip.

^* Yes, yes, light waves require no medium and can travel through a vacuum. They are a special case.

As we will see, the mathematical description of waves should look very familiar to you, now that you have been studying simple harmonic motion.

One of the most important properties of waves is that they carry energy from one location to another.

In case we have time ...