# Topic 4: Waves

## 4.1 Oscillations

Simple harmonic motion. What is it? Well, it’s a specific type of jiggling, where the magnitude of the acceleration is directly proportional to the distance displaced from equilibrium. That is,

a propto x

Think of a pendulum. The acceleration and displacement are in opposite directions. That’s sensible. If the acceleration and displacement were in the same direction, it would just fly off. Not much in the way of jiggling. Hence, there’s a negative sign in the equation. Now, we’re going to let the constant of proportionality be omega2. Why square? It’s convenient. You’ll see in a bit.

Now, let’s say we want to find out where the pendulum will be at any given time. We need to find the displacement as a function of time. So we solve the differential equation above (you can look it up, it’s not covered in this syllabus), and we get

x = x0 sin wt

Where x0 is the amplitude.

So now we’ve got the displacement. If we differentiate that with respect to time once, we get the velocity. If we do it again, we get the acceleration as a function of time. Earlier we had acceleration as a function of displacement, which may not be so useful in some situations.

Period, frequency, wavelength (Show on a graph).

Displacement time graphs vs displacement distance graphs. Displacement-time graphs track the motion of a single particle on the wave; that is, how the position of a given particle changes with time. Displacement-distance graphs, on the other hand, are more like photographs. You get to see all the particles and their positions, the entire wave, all at once. Now, the only way we can do that is by taking a snapshot, ie, when time is set still.

## 4.2 Traveling waves

transverse, longitudinal

wave speed (as a function of f and lambda)

sound and EM waves

## 4.3 Wave characteristics

Wavefronts and rays

Amplitude and intensity (inverse square law)

Polarisation (methods, maybe types. Malus law)

4.4 Wave behaviour

Reflection, refraction, Snell’s law, critical angle, total internal reflection (I should make a gif)

single slit

double slit

## 4.5 Standing waves

How they are formed, how they differ from travelling waves

Strings and pipes (shape, frequency, wavelength and L, fixed and free boundaries)