## Basics

Waves are oscillations of a medium that transfer energy. The only exception is that of standing waves which is covered later. Sound waves, electromagnetic waves and seismic waves are just a few examples. Despite the great variance in wave types they all share the same basic aspects that repeat over space:

The speed of the wave (c) is the distance a part of the wave travels in a certain time. The wavelength (λ) is the physical distance between the two identical parts of a wave, in the diagram above it is being shown between two peaks but any identical parts will do. The number of full waves (one segment of the repeating pattern) that pass a point every second is called the frequency (f), this is closely related to period (T) which is the time taken for a full wave to pass a point as they are both inverses of each other. The amplitude (A, but given y in the diagram) is the displacement of the medium from its normal position. The maximum displacement upwards is called the peak and the maximum downwards is called the trough. Although the diagram above presents this displacement as upwards on the graph, this is no guarantee the particles themselves are moving upwards.

## Transverse and Longitudinal

Travelling waves (all waves that aren’t standing) come in two main types. Transverse waves are the ones we are most familiar with where the medium goes up and down. This of course means that the wave itself travels at a right angle to the displacement of the medium. It is important to understand that none of the media actually travels with the wave. The individual particles go up and down but they merely pass on the energy and it is this energy that is the wave.

Longitudinal waves have their particles displaced in the same direction, in other words parallel, to the wave. Once again the particles move back and forth but ultimately stay oscillating around a fixed point, the rings on the slinky do not carry on moving down as the wave progresses:

Wave (a) is longitudinal and wave (b) is transverse. Longitudinal waves include sound waves, waves in springs, atoms oscillating in structures and seismic primary (P) waves. Transverse waves include the entire electromagnetic spectrum, strings on instruments, ripples on water and seismic secondary (S) waves.

## Properties of Waves

All waves demonstrate four primary characteristics:

• They can be reflected
• They can be refracted
• They can be diffracted
• They can interfere

Reflection is simple to understand. A wave incident on a surface will bounce off it leaving at the same angle it came in at. There are more complicated details involving the idea that some bounces are “hard” and others are “soft” but this is unnecessary information at the moment.

Refraction is what is witnessed in a glass block when a light beam or a laser passes into it. As the wave (in this case electromagnetic) travels at different speeds in the two materials, a direction change is required to conserve momentum.

Diffraction, although sounding similar to refraction, is completely different. When a wave passes near to a corner or through a gap it spreads out on the other side. This is why sound can be heard even when you can’t see the person speaking.

Interference is essential for understanding the next section. When two waves “collide” with each other the medium at the collision point will get told to do two things by the two different waves. If both waves tell the medium to move up, then the medium will move up twice as much. If one instructs the medium to move up and the other to move down then no movement will occur at all. The first case is called constructive interference as the resultant wave is bigger, while the second case is called destructive interference as the resultant is no wave at all. In the diagram this is represented as the peaks either lining up with other peaks or with troughs.

## Standing Waves

Standing waves have already been mentioned as waves that do not transfer any energy. This is visually seen as the fact the wave doesn’t seem to move but simply stand in its place.

The faint lines in the diagram represent the positions of a plucked string over one cycle. It moves down and up again but the position of the peak doesn’t move. The stationary points, called nodes, will always be nodes and will never move along the string. The antinode, the place of maximum displacement, will always be where the string has maximum displacement.

The reason these unmoving waves form, and the reason they don’t carry any energy, is actually because they are two waves, perfectly identical, travelling in opposite directions, interfering with each other. Although this is hard to visualise luckily there is this animation from The Physics Classroom, which should hopefully clear things up.

The four different waves shown in the diagram are often called, going down the diagram: the fundamental or first harmonic, the second harmonic, the third harmonic, the fourth harmonic and the pattern continues for even more nodes being present.