# GCSE & A Level Revision Notes

## Wave motion

A progressive wave is one that moves away from a source – transferring energy. This can be through movement of particles (up and down, or side to side) or radiation. In transverse waves, the particles oscillate perpendicular to the direction of the wave, whereas in longitudinal waves, the oscillations are parallel to the direction of wave motion.

Displacement – The distance moved by a particle from the rest position – it is a vector, measured on the y axis.

Amplitude – This is the maximum displacement of any point on the wave. It is scalar.

Wavelength – The distance between two points on the wave that are in phase (have the same motion). We can measure wavelength from a photograph or a displacement-distance graph (compression to compression on a photo of a longitudinal wave, and peak to peak on a displacement-distance graph of a transverse wave).

Period – The time taken for one complete pattern of oscillation to pass a point. This can be measured on a displacement-time graph.

Phase Difference – The relationship between the patterns of vibration at two points on the wave. Two points that have identical oscillations are said to be in phase, whereas two points that have opposite motion are said to be in antiphase. It is either measured in degrees or radians, where 2π = 360o. Any even multiple of π or multiple of 360 means that the waves are in phase.

Frequency – The number of waves that pass a point per unit time.

Speed – The distance travelled by the wave per unit time.

Speed = distance/time

In one full oscillation of the source, the wave will move by a distance of one wavelength, which takes a time of one period.

Therefore:

You can predict the motion of a particle on a wave by looking at its graph. On a displacement-distance graph, look towards the source of the wave. In a displacement-time graph, look towards the future of the graph.

Reflection – Waves are reflected when they rebound from a barrier, changing direction, but remaining in the same medium. When waves reflect, the angle of incidence is always equal to the angle of reflection. This can be represented by a ray, or a series of wave fronts, which are perpendicular to the ray.

Refraction – If a wave is transmitted into a new medium AND the ray hits the boundary at an angle less than the critical angle, the ray will refract. If a ray is entering a glass block, its speed decreases, and it bends towards the normal. Inside the block, the frequency is unchanged, but the wavelength decreases. Leaving the block again, the speed increases, and so the ray speeds away from the normal.

Diffraction – Diffraction is the spreading out of waves when they encounter a gap, or a small boundary.
The closer the size of the gap to the wavelength, the greater the diffraction. Diffraction is greatest when the size of the gap is equal to the wavelength.

## Electromagnetic Waves

Electromagnetic waves are those that travel through the electric and magnetic fields of the universe. There are two transverse parts to an EM wave, travelling at 90o to each other, one in the electric field and one in the magnetic field.

All EM waves are transverse and can travel in a vacuum. They all have different frequencies and wavelengths but all travel at 3x108 m/s in a vacuum. There is a trend, going down the spectrum of increasing frequency and energy, but decreasing wavelength.

Name Wavelength (m) Frequency (hz) Uses Dangers
Radio waves 1 3 x 10 8 Communications None significant
Microwaves 0.01 3 x 10 10 Communications, Cooking TV Remotes, Heat Detectiion Internal tissue heating. Burning
Infra-Red radiation 1 x 10 -4 3 x 10 12 Night Vision None significant
Visible Light (Red) 6.5 x 10 -7 4.6 x 10 14 Optical Communication and photography Retina damage
Visble Light (Blue) 4.5 x 10 -7 6.7 x 10 14 Optical Communication and photography Retina damage
Ultraviolet 1 x 10 -7 3 x 10 15 Security markings, Detecting forgeries & Killing bacteria Skin Cancer, blindness and sunburn
X-rays 1 x 10 -9 3 x 10 17 Medical Imaging, Security Ionising radiation causes cell damage leading to cancer
Gamma rays 1 x 10 -9 1 x 10 18 Sterilisation, Cancer treatments Ionising radition causes cell damage leading to cancer

There are three types of ultraviolet (UV) light emitted from the sun – UV-A, UV-B and UV-C. UV-A accounts for 99% of UV light, and has a wavelength of 315-400nm, which causes tanning. UV-B causes damage such as skin cancer and sunburn and has a wavelength of 280-315nm, and UV-C is the most dangerous (wavelength 100-280 nm), which is completely filtered out by the ozone layer. Sun cream contains filters which filter UV-B, to prevent sunburn. Glass absorbs UV, which is why you don’t get sunburnt from sitting in doors.

A plane-polarised wave is a transverse wave that only oscillates in one direction. Longitudinal waves cannot be polarised, as their oscillations are always in the same direction as wave travel. Electromagnetic waves can be polarised by a Polaroid – a piece of material that will only allow light of a specific polarisation to pass through.

When light is reflected, it is partially polarised, this can be used in cameras and sunglasses to prevent glare. Polaroids are also used in 3D movies, the glasses are Polaroids with perpendicular transmission axes, and then the film is slightly offset and played in sync, and each eye only picks up one of the images, which makes the brain think it is 3D. Polaroids are also used in stress analysis – materials like Perspex can rotate the polarisation state of light, the amount is affected by the stress in the material.

Malus’s Law:

Malus’s law tells us how much polarised light will pass through a Polaroid as it is rotated. To test this, we use two Polaroids (a polariser and an analyser).

As the analyser is rotated, the detector shows maxima and minima. There are maxima at 0o, 180 o and 360 o and minima at 90 o and 270 o.

The transmitted intensity through the analyser is directly proportional to

## Interference

The Principle of Superposition: When two or more waves of the same type exist in the same place, the resultant wave is found by adding the vector sum of the displacements of each individual wave.

The principle of superposition can be illustrated graphically, which is shown by this diagram.

Interference – The addition of two or more waves (superposition) to form a new wave pattern.

Coherence – If two waves have a constant phase relationship, they are said to be coherent.

Path Difference – You can alter the path of a wave in order to change the interference pattern formed. The difference between the paths of two waves is known as the path difference.

Phase Difference – The difference between the movements of two waves. If waves are completely out of phase, one will be one wavelength behind the other.

There are two types of interference, constructive and destructive. If the path difference is a whole number of wavelengths, then the two waves will be in phase, and so there will be constructive interference. If the path difference is an odd half multiple of a wavelength, then the two waves will arrive in antiphase, and therefore there will be destructive interference, as the two waves will cancel each other out.