# Waves

2.1.1 Progressive and Stationary Waves
A progressive wave is one where the wave moves from one point to another, and a stationary wave is one where a wave is trapped between two boundaries and re ects back on itself.
2.1.2 Transverse and Longitudinal Waves
A transverse waves is one where the vibration is perpendicular to propagation of the wave and a longitudinal wave is one where the vibration is parallel to the propagation of the wave.
2.1.3 Polarisation
Polarisation is where transverse waves such as light, and microwaves are attenuated (reduced in energy), by reducing the number of planes which they exist in (often to only one, which is known as plain polarised) by using a polaroid to block out all the waves in other planes reducing the number of planes which the wave exists in. This attenuation does not result in any loss of signal, but the bars of the polaroid often get hot, since the polaroid is absorbing the energy from those waves which it blocks.
2.1.4 Displacement, amplitude, wavelength, frequency, time period and velocity of a wave
Here are de nitions of the main key terms for progressive waves:
Displacement, x The straight distance from the equilibrium position
Amplitude, A The maximum displacement
Wavelength, λ The horizontal distance between corresponding points on adjacent waves

Frequency, f The number of oscillations per second (you can only calculate f, it is not found on any graph)
Period Time, T The time taken for one complete oscillation
Velocity, v Velocity is the speed at which the wave travels through a media

2.1.7 Principle of Superposition
The principle of superposition states that when two waves overlap, their displacements add. This only happens when two waves of the same type overlap. This course only covers coherent waves overlapping.
2.1.8 Interference
An interference pattern is what you would observe if superposition had occurred, constructive interference occurs when the waves meet in-phase, so peaks meet peaks and troughs meet troughs, so max amplitude occurs, destructive interference occurs when waves meet in anti-phase, so peaks meet troughs and vice versa, minimum amplitude occurs.
2.1.9 Single-slit Interference (di raction)
A wave will spread out when it passes through a gap or boundary, this is known as di raction. For noticeable e ects, the gap must roughly equal the wavelength. The observed pattern shows one wide very bright central fringe, with thinner less bright fringes. The formula for it is:

2.1.10 Double-slit Interference
Young’s double-slit experiment was the rst piece of experimental evidence that light is a wave. A source of light was incident on a two adjacent slits with equal width. The two di raction patterns from the two slits overlap and superposition occurs. Just like a single slit, there are a series of dark and light fringes cause by constructive and destructive interference. The interaction of light showed that it was a wave. However, the what is noticeable is that the peaks are not equal height, because the single slit pattern `restricts’ the double slit. This experiment can be demonstrated with water waves, sound waves and microwaves. The double slit formula is:

2.1.11 Path Di erence
Path di erence is the di erence in metres between the lengths of two paths (the distance along the wave).
2.1.12 Phase Di erence
Phase relates the relative motion of one part of a wave compared to another OR the relative motion of one part of a wave and one part of a second wave at a certain point. A full wavelength is 360◦ of phase. `In phase’ occurs at whole multiples of the wavelength (nλ). This means the two points studied, are moving at the same velocity, meaning speed and direction. `In anti-phase’ occurs at whole plus half multiples (n + 1 2λ) of a wavelength. This means the two points studied, are moving with the same speed but travel in opposite directions.
2.1.13 Coherence
Coherence is when two waves have constant phase di erence, which is achieved by having the same frequency.
2.1.14 Conditions for two-source Interference
The conditions for two-source interference are constant phase di erence and vibrations in the same line.

2.1.15 Di raction Grating
A di raction grating is a large number of parallel slits that are simultaneously illuminated, because there are so many slits, there are many waves which interfere and so constructive interference is rare and so maxima are rare, each maxima is known as an order. Di erent wavelengths give di erent patterns, so a di raction grating can split up multi-coloured light into it’s constituents. This is how we identify what makes up stars. The formula for di raction gratings is:
dsinθ = nλ
where n is the order number, d is the distance between the slits and θ is the angle from the 0th order

2.1.16 Di raction of a Multicoloured Source
Gas can be made to emit light, and whilst it appears monochromatic, it isn’t, it is a mixture of certain colours, the more colours involved, the more complicated the gas. These colours are split up by the di raction grating because the colours have di erent wavelengths, they have di erent rst orders and so they can be seen separately.
2.1.17 Coherent and Incoherent sources
Examples of coherent sources include lasers, Lloyd’s mirror and Fresnel’s biprism. Examples of incoherent sources include Sodium arc lamps used in street lamps, black bodies (more on page 34) and acoustic white noise which radiates incoherent sound waves.
2.1.18 Stationary/Standing Waves
A standing is produced when a wave re ects from a boundary and interferes with the oncoming waves. If the boundary is xed, the wave does not make the boundary vibrate, if it is an open boundary, the wave does make the boundary vibrate. Re ection from a xed boundary

always occurs in anti-phase, so destructive interference occurs and so you get zero displacement which is an area known as a node. Re ection from an open boundary is always in phase, so constructive interference occurs and so you get maximum displacement, which is an area known as an anti-node.
2.1.19 Harmonics
There are three types of systems, and in each, there are harmonics, where the rst occurs at the fundamental frequency (f0) with the wavelength equal to twice (or four times in the case of xed open) the length of the system (l). Each following harmonic is a multiple of f0 and has another node (with the rst harmonic beginning with the minimum number) and the required number of anti-nodes. The inter-nodal distance is λ 2 and a stationary wave can be regarded as a superposition of two progressive waves of equal amplitude and frequency.