Understanding Wave Properties

• Progressive waves transfer energy without transferring any material
• Progressive waves are made up of particles of a medium oscillating

Progressive waves

• Amplitude is a wave's maximum displacement from the equilibrium position, measured in meters (m)
• Frequency (f) is the number of complete oscillations passing a point per second, measured in Hertz (Hz)
• Wavelength (λ) is the length of one whole oscillation and is measured in meters (m)
• Speed (c) is the distance travelled by the wave per unit time, measured in meters per second (m/s)
• Phase is the position of a point on a wave cycle, measured in radians, degrees, or fractions of a cycle
• Phase difference measures how much a particle/wave lags behind another, measured in radians, degrees, or fractions of a cycle
• Period (T) is the time taken for one full oscillation, measured in seconds (s)
• A pair of points on a wave are in phase if they are both at the same point in their wave cycle, have the same displacement and velocity, and their phase difference is a multiple of 360° (2π radians)
• Points don't need to have the same amplitude to be in phase, only the same frequency and wavelength
• A pair of points are completely out of phase when they're an odd integer of half cycles apart
• The speed of a wave equals its frequency multiplied by its wavelength: c = fλ
• Frequency of a wave is the inverse of its period: f = 1/T

Transverse and Longitudinal Waves

• Transverse waves have particles oscillating at right angles to the direction of energy transfer
• All electromagnetic (EM) waves are transverse, traveling at 3 x 10^8 m/s in a vacuum
• Transverse waves can be demonstrated by shaking a slinky vertically
• Longitudinal waves have particles oscillating in parallel to the direction of energy transfer
• Longitudinal waves are made up of compressions and rarefactions and cannot travel in a vacuum
• Sound is a longitudinal wave, demonstrated by pushing a slinky horizontally

Polarisation

• Polarised waves oscillate in only one plane, and only transverse waves can be polarized
• Polarization provides evidence for the nature of transverse waves as it can only occur if a wave's oscillations are perpendicular to its travel direction
• Polaroid sunglasses reduce glare by blocking partially polarised light reflected from surfaces such as water and tarmac
• TV and radio signals are usually plane-polarised via the orientation of rods on the transmitting aerial
• The receiving aerial must be aligned in the same plane of polarisation to receive the signal at full strength

Superposition

• Superposition describes where the displacements of two waves are combined as they pass each other
• The resultant displacement is the vector sum of each wave's displacement
• Constructive interference occurs when two waves have displacement in the same direction
• Destructive interference occurs when one wave has positive displacement, and the other has negative displacement
• Total destructive interference occurs if equal waves have opposite displacements

Stationary Waves

• Stationary waves are formed by superposing two progressive waves travelling in opposite directions in the same plane, with the same frequency, wavelength, and amplitude
• No energy is transferred by a stationary wave
• Antinodes are formed where the waves constructively interfere and are regions of maximum amplitude
• Nodes are formed where the waves destructively interfere, and are regions of no displacement
• The lowest frequency that forms a stationary wave is the first harmonic, which forms a stationary wave with two nodes and a single antinode
• The distance between adjacent nodes (or antinodes) is half a wavelength (for any harmonic)
• A stationary wave is formed if one end of a string is fixed to a driving oscillator
• A wave travelling down the string from the oscillator will be reflected at the fixed end of the string
• Reflected waves travel back along the original string, causing superposition
• The frequency to calculate stationary wave: f = (1/2L) * √(T/µ) where L is the length of the vibrating string, T is the tension, and µ is the mass per unit length.
• The first harmonic frequency can be doubled to find the second harmonic where there are 2 antinodes
• The first harmonic frequency can be tripled to find the third harmonic frequency where there are 3 antinodes
• Stationary microwaves are formed by reflecting a microwave beam at a metal plate using a microwave probe to find the nodes and antinodes
• Stationary sound waves are formed by placing a speaker at one end of a closed glass tube, then laying powder across the bottom
• The powder will be shaken at the antinodes and settle at the nodes
• Since wavelength is twice the distance between each node, and the frequency of the signal generator is known the speed of sound in air can be found (c = fλ)

Interference

• Path difference refers to the difference in the distance travelled by two waves
• Coherent sources have the same frequency and wavelength, in addition to a fixed phase difference
• Lasers are coherent and monochromatic light sources, emitting a single wavelength of light
• Young's double slit experiment demonstrates interference of light from two coherent sources
• The double slit experiment can be performed using two coherent light sources, or a single source and a then double slit in its path
• If a non-coherent light source is used, a single slit can be put in place before the double slit
• The procedure for Young's double slit experiment:
• Shine a coherent light source through 2 slits around the same size as the wavelength of the laser light, so the light diffracts
• Each slit acts as a coherent point source, creating light and dark fringes
• Light fringes form when the light meets in phase and undergoes constructive interference
• Light fringes occur where the path difference between waves is a whole number of wavelengths (nλ, where n is an integer)
• Dark fringes form where the light meets completely out of phase and undergoes destructive interference
• Dark fringes are formed where the path difference is a whole number and a half wavelengths ((n+½)λ)
• Formula for Young's double slit experiment: W = (λD) / s, where W is the fringe spacing, λ is the wavelength, D is the distance to the screen, and s is the slit separation
• Using white light gives wider maxima and a less intense diffraction pattern with a central white fringe
• White light irradiation will create spectra in the alternating fringes, where violet is closest/red furthest from the central maximum

Laser Safety

• Lasers can permanently damage eyesight, laser safety precautions:
• Wear safety goggles
• Don't shine laser at reflective surfaces
• Display warning sign
• Never shine laser at a person

Wave Nature of light and Sound

• The use of two speakers connected to the same signal generator could be used instead of using a double slit
• Using this setup the intensity of the waves can be measured with a microphone that is equivalent to dark fringes
• Evidence for the wave nature of light was proved by Young's double slit experiment because diffraction and interference are wave properties
• Therefore EM radiation must act as a wave

Diffraction

• Diffraction is the spreading out of waves when they pass through or around a gap
• Greatest diffraction occurs when the gap is around the same size as the wavelength
• Most waves are reflected when the gap is smaller than the wavelength, whereas there is less noticeable diffraction when the gap is larger
• Wider obstacles produce less diffraction
• Monochromatic light diffracted through a single slit onto a screen forms an interference pattern of light and dark fringes
• The interference pattern created from monochromatic light has a bright central fringe, which is double the width of all other fringes, with alternating dark and bright fringes on either side
• Bright fringes are created where the waves are constructively interfering, whereas dark fringes are caused by destructive interference
• When using white light, different spectrums of colour become present, where violet is closest to the central maximum and red is furthest
• Increasing the slit width decreases the amount of diffraction, as the central maximum becomes narrower and its intensity increases
• Increasing the light wavelength will also increase the amount of diffraction, as the slit is closer in size to the light's the central maximum becomes wider and its intensity decreases
• A diffraction grating contains many equally spaced slits very close together on a slide
• When monochromatic light is passed through the diffraction grating interference pattern is much sharper and brighter than it would be after being passed through a double slit
• The zero order line is the ray of light passing through the centre of a diffraction grading
• First order lines are lines on either side of the zero order
• Second order lines are the lines outside the two first order lines
• The formula associated with diffraction gratings is d sin θ = nλ, where d is the distance between the slits, θ is the angle to the normal made by the maximum, n is the order, and λ is the wavelength
• As λ increases (by changing light from blue to red), the distance between the orders will increase because θ is larger
• As slit spacing is closer in size to the wavelength, diffraction will spread out,
• The maximum value of sin θ is 1, therefore, any values of n which give sin θ as greater than 1 are impossible

Diffraction Application

• Diffraction gratings split up light from stars to get line absorption spectra, showing which elements are present in the star
• X-ray crystallography directs x-rays at a thin crystal sheet to act as a diffraction grating, forming a diffraction pattern
• The wavelength of x-rays is comparable to the gaps between atoms so this diffraction pattern can be used to measure the atomic spacing in the crystal material

Refraction

• Refractive index (n) is a property of a material that measures how much it slows down light: n = c/cs, where c is the speed of light in a vacuum and cs is the speed of light in the substance
• Materials wth a higher refractive index are more optically dense
• Light doesn't slow down significantly when travelling in the air compared to travelling through a vacuum, so the refractive index of air is approximately 1
• Refraction occurs when a wave enters a different medium, causing it to change direction

Snell's Law

• Snell's Law formulas for refraction of light: n₁sinθ₁ = n₂sinθ₂, where n₁ is the refractive index of material 1, n₂ is the refractive index of material 2, θ₁ is the angle of incidence in material 1, and θ₂ is the angle of refraction in material 2
• The light changes speed as it moves across the boundary between two materials, causing it to change direction

TIR

• Refraction causes light to slow down and bend towards the normal when moving to a more optically dense medium. If moving to less optically dense medium, light bends away from normal
• As the angle of incidence increases so does the angle of refraction increases
• Refraction angle increases to 90° when the incident ray is at the critical angle
• The critical angle can be calculated using: sin θc = n2/n1, where n₁ > n₂
• Total internal reflection (TIR) happens when the angle of incidence is greater than the critical angle and the incident refractive index (n₁) is greater than the refractive index of the material (n₂)

Optical Fibres

• Optical fibres are a useful application of total internal reflection: flexible, thin tubes of plastic/glass carry information in the form of light signals
• Optical fibres have an optically dense core surrounded by cladding with a lower optical density allowing TIR to occur
• Cladding protects the care from damage to reduce signal degradation of light escaping the core, which can cause information to be lost

Signal Degradation

• Signal degradation can be caused by absorption of signal's energy by the fibre reducing the amplitude
• Signal degradation can be caused by dispersion leading pulse broadening of the received pulse
• Modal dispersion is caused by light rays entering the fibre at different angles, meaning they take different paths
• The rays in modal dispersion will be travelling at differing speeds, causing the pulses to broaden
• Modal dispersion can be reduced using a very narrow core
• Material dispersion is caused by light having differing wavelengths within and thus travel speeds within a single pulse
• Material dispersion caused by this can be prevented when using monochromatic light
• Using an optical fibre repeater can reduce both absorption and dispersion, regenerates the signal during its travel to its destination