waves Flashcards
progressive wave
A wave that transfers energy from one point to another without transferring the medium itself
ways you can tell waves carry energy:
- Electromagnetic waves cause things to heat up.
- X-rays and gamma rays knock electrons out of their orbits, causing ionisation.
- Loud sounds cause large oscillations of air particles which can make things vibrate.
- Wave power can be used to generate electricity.
Reflection
The wave is bounced back when it hits a boundary. E.g. you can see the reflection of light in mirrors.
Properties of a Progressive Wave - Displacement (x)
Displacement (x) of a wave is the distance of a point on the wave from its equilibrium position
It is a vector quantity; it can be positive or negative
Properties of a Progressive Wave - Amplitude (A)
Amplitude (A) is the maximum displacement of the wave from its equilibrium position
Properties of a Progressive Wave - Wavelength (Ξ»)
Wavelength (Ξ») is the distance between points on successive oscillations of the wave that are in phase
These are all measured in metres (m)
Properties of a Progressive Wave - Period (T)
Period (T) or time period, is the time taken for one complete oscillation or cycle of the wave
Measured in seconds (s)
Properties of a Progressive Wave - Frequency (f)
The number of complete waves passing a point in one second.
The unit of frequency is the hertz (Hz) or s-1
Properties of a Progressive Wave - Speed (v)
Speed (v) is the distance travelled by the wave per unit time
Measured in metres per second (m s-1)
wave equation
The wave equation links the speed, frequency and wavelength of a wave
This is relevant for both transverse and longitudinal waves
Phase Difference between 2 waves
Phase specifies the position of point within a wave cycle.
Phase difference is the fraction of a cycle a particle/wave lags behind another particle/wave. It is measured in radians, degrees or fractions of a cycle.
When the crests or troughs are aligned, the waves are in phase
When the crest of one wave aligns with the trough of another, they are in antiphase
Electromagnetic wave speed in a vacuum
You may have seen c used before as the speed of light in a vacuum.
All electromagnetic waves, including light, travel at a speed of c = 3.00 Γ 108 m/s in a vacuum.
Measuring the speed of sound
The speed of sound can be measured in a laboratory in a number of different ways. One of the easiest methods is to use two microphones in a straight line a distance d apart. The microphones should have separate inputs so the signals from each can be recorded separately.
Use the signal generator to produce a sound from the loudspeaker and use the computer to record the time between the first and second microphone picking up the sound. Do this by measuring the time delay between the first peak of the signal received by each microphone on a graph of voltage against time
You can then use speed = distance Γ· time to calculate the speed of the sound waves. You should repeat this experiment multiple times and take an average of your results.
Measuring wave speed in water
Start by recording the depth of water in the tank using a ruler.
Use the ripple tank dipper to create vibrations with a regular frequency in the tank. Dim the main lights in the room and turn on the strobe light (a light that flashes periodically).
Increase the frequency of the strobe light from zero until the waves appear to be standing still. When this happens, the frequency of the strobe light is equal to the frequency of the water waves.
Use a ruler on the white paper below the tank to measure the distance between two adjacent peaks. You could make this measurement more precise by measuring the distance between several peaks and dividing this by the number of troughs in between. The distance between two adjacent
peaks is equal to the wavelength, 1, so you can use the wave equation c = fl
to calculate the speed of the waves.
Repeat this experiment for a range of water depths, measuring the wavelength and calculating the wave speed each time.
You should observe that the waves travel quicker in deeper water.
transverse waves
In transverse waves the displacement of the particles or field (i.e. the vibration or oscillation) is perpendicular to the direction of energy propagation (transfer).
All electromagnetic waves are transverse. They travel as oscillating magnetic and electric fields and can be polarised.
Other examples of transverse waves are ripples on water, waves on strings, and some types of earthquake shock wave (S-waves).
Drawing transverse waves
There are two main ways of drawing transverse waves:
They can be shown as graphs of displacement against distance along the path of the wave.
Or they can be shown as graphs of displacement against time for a point as the wave passes. Both sorts of graph often give the same shape.
Displacements upwards from the centre line are given a + sign. Displacements downwards are given a - sign.
Longitudinal waves
In longitudinal waves the displacement of the particles or fields (the vibration) is along the direction of energy propagation.
The most common example of a longitudinal wave is sound.
A sound wave consists of alternate compressions and
rarefactions of the medium itβs travelling through (thatβs why sound canβt travel in a vacuum).
Some types of earthquake shock waves are also longitudinal (P-waves).
Describe the nature of an unpolarised wave
Oscillation of particles / field are pendicular to the direction of energy propogation (i.e. they are transverse waves) and the oscillations exist in more than a single plane.
Polarisation
Polarisation is when:
Particle oscillations occur in only one of the multiple directions perpendicular to the direction of wave propagation
Polarisation can only occur in transverse waves (not longitudinal waves)
This is because transverse waves oscillate in any plane perpendicular to the propagation direction
When transverse waves are polarised, this means:
Vibrations are restricted to one direction
These vibrations are still perpendicular to the direction of propagation / energy transfer
How are waves polarised
Waves can be polarised through a polariser or polarising filter
A polarising filter will only allow waves polarised in a particular plane to pass through
Diagram A shows that only unpolarised waves can be polarised.
When unpolarised light passes through a polariser, the intensity is reduced by 50%
Diagram B shows that when a polarised wave passes through a filter with a transmission axis perpendicular to the wave, none of the wave will pass through
Light can also be partially polarised through reflection, refraction and scattering
Investigating Light Intensity with Two Polarisers - parallel transmission axes
If an unpolarised light source is placed in front of two identical polarising filters, A and B, with their transmission axes parallel:
Filter A will polarise the light in a certain axis
All of the polarised light will pass through filter B unaffected
In this case, the maximum intensity of light is transmitted
Investigating Light Intensity with Two Polarisers - perpendicular transmission axes
As the polarising filter B is rotated anticlockwise, the intensity of the light observed changes periodically depending on the angle B is rotated through
When A and B have their transmission axes perpendicular to each other:
Filter A will polarise the light in a certain axis
This time none of the polarised light will pass through filter B
In this case, the minimum intensity of light is transmitted
Light intensity vs angle of second polariser
The resulting graph of the light intensity with angle, as the second polariser is rotated through 360Β°, looks as follows:
Applications of Polarisers - Polaroid Sunglasses
Polaroid sunglasses are glasses containing lens with polarising filters with transmission axes that are vertically oriented
This means the glasses do not allow any horizontally polarised light to pass through
Light reflected from surfaces tends to be polarised in the plane parallel to the surface
polaroid sunglasses are useful in reducing the glare off reflective surfaces as the partially-polarised light will be eliminated by the polarising filter reducing the overall intensity by 50%.
As a result of this, objects under the surface of the water can be viewed more clearly
partial plane polarisation
When light is reflected from a reflective surface e.g. the surface of water or a wet road, it undergoes partial plane polarisation
This means if the surface is horizontal, a proportion of the reflected light will oscillate more in the horizontal plane than the vertical plane
Polaroid Photography
Polaroid cameras work in the same way as polaroid sunglasses
They are very useful for capturing intensified colour and reducing glare on particularly bright sunny days
Vertically polarised filters also enable photographers to take photos of objects underwater
This is because the light reflected on the surface of the water is partially polarised in the horizontal plane
This glare is eliminated by the Vertically polarising lens
However, the light from the underwater object is refracted by the surface of the water, not reflected, so it is not plane-polarised
Therefore, the light from the underwater object is more intense than the glare and shows up much more brightly in the photo
Polarisation of Radio & Microwave Signals
Radio and television services sent as radio waves are almost always plane polarised, so a receiving antenna needs to be aligned with the plane of the wave from the transmitter to obtain the strongest signal.
The particular orientation of a receiving antenna will depend on the transmitter it is pointing towards and the polarity of the services being broadcast
What direction is point X about to move as the wave moves to the right
downwards (Hint: draw the wave moving forward a little)
What direction is point X about to move as the wave moves to the left
Upwards
What direction is point Q about to move as the wave moves to the right?
To the left
Particles in rarefactions travel opposite to the direction of energy transfer
What direction is point P about to move as the wave moves to the right?
To the right
Particles in compressions travel in the direction of energy transfer
The principle of superposition
The principle of superposition says that when two or more waves cross, the resultant displacement equals the vector sum of the individual displacements.
You can use the same idea in reverse β a complex wave can be separated out mathematically into several simple sine waves of various sizes.
Constructive interference
When two waves meet, if their displacements are in the same direction, the displacements combine to give a bigger displacement. A crest plus a crest gives a bigger crest. A trough plus a trough gives a bigger trough.
Destructive interference
If a wave with a positive displacement (crest) meets a wave with a negative displacement (trough), they will undergo destructive interference and cancel each other out. The displacement of the combined wave is found by adding the displacements of the two waves
What is a stationary wave?
A stationary (standing) wave is the superposition of two overlapping progressive waves with the same frequency and amplitude, moving in opposite directions.
Unlike progressive waves, no energy is transmitted by a stationary wave.
Nodes & Antinodes on stationary waves
A stationary wave is made up nodes and antinodes
At points where the two waves are in antiphase a node (0 amplitude) forms. Nodes are regions where there is no vibration.
At points where the waves are in phase an antinode (maximum amplitude) forms.
The nodes and antinodes do not move along the string.
Nodes are fixed and antinodes only move in the vertical direction.
No energy is transferred along the wave, it just oscillates between the kinetic and potential stores of the medium
Examples of Stationary Waves
- Vibrations caused by stationary waves on a stretched string produce sound
- This can be demonstrated by a length of string under tension fixed at one end and vibrations made by an oscillator:
- The wave generated by the oscillator is reflected back and forth.
- At specific frequencies, known as resonant frequencies, a whole number of half wavelengths will fit on the length of the string
- As the resonant frequencies of the oscillator are achieved, stationary waves form
A string is stretched between two fixed posts, and excited with a vibration generator. A stationary wave forms on the string. Describe and explain how the stationary wave forms, and how the processes which form it give rise to the features of a stationary wave
There are 2 overlapping waves - same frequency, wavelength, speed and amplitude but opposite direction of travel - one is the reflection of another off the fixed ends.
The waves superpose.
Nodes (0 amplitude) form when phase difference = 0 radians
anti Nodes (max amplitude) form when phase difference = pi radians
no energy transfer along the string
Points on a stationary wave can only ever be in phase or in antiphase with one another
Resonant frequencies
A stationary wave is only formed at a resonant frequency (when an exact number of half wavelengths fits on the string). There are some special names for each resonant frequency.
harmonics: fundamental frequency & 2nd 3rd and 4th harmonic
As the frequency of the vibration generator increases, different stationary waves are set up.. The first stationary wave will occur on a string of length L when the generator is vibrating at the fundamental frequency, f0, of the string.
formula for frequency of the 1st harmonic
formula for frequency of the 2nd & 3rd harmonic
Stationary microwaves
You can set up a stationary wave by reflecting a microwave beam at a metal plate. The superposition of the wave and its reflection produces a stationary wave. You can find the nodes and antinodes by moving the probe between the transmitter and reflecting plate. The meter or loudspeaker receives no signal at the nodes and maximum signal at the
antinodes.
Stationary sound waves
Powder in a tube of air can show stationary sound waves. A loudspeaker produces stationary sound waves in the glass tube. The powder laid along the bottom of the tube is shaken
away from the antinodes but left undisturbed at the nodes.
The distance d between each pile of powder (node) is Ξ» / 2, so the speed of sound c = fΞ» is equal to c = f x 2d = 2df. So the speed of sound can be calculated by measuring d and knowing the frequency of the signal generator.
Stationary waves in pipes
A sound wave can be reflected by an open or a closed end of a pipe
Closed ends form nodes, while open ends form antinodes
Diffraction
The spreading out of waves when they pass through a gap or by an edge
It occurs when the size of the aperture or obstacle is of the same order of magnitude as the wavelength of the incident wave.
- The longer the wavelength the greater the diffraction.
- The smaller the aperture the greater the diffraction
Coherent sources
a particular example of superposition when both waves have a CONSTANT PHASE DIFFERENCE and SAME FREQUENCY
these waves are said to be coherent
constructive interference of 2 coherent sources
For coherent sources, for any point where the path difference between the waves is a whole number of wavelengths, the phase difference between the waves will be 0 or an integer multiple of 2Ο, so the waves arrive in phase and superpose to give a large amplitude wave - a maximum
Destructive interference of 2 coherent sources
For coherent sources, for any point where the path difference between the waves is (n+0.5)Ξ»
where n is an integer i.e. 0.5Ξ», 1.5Ξ», 2.5Ξ»,
the phase difference between the waves will be an odd multiple of Ο, so the waves arrive in antiphase and superpose to give a low amplitude wave β a minimum.
If the two waves have the same amplitude at that point in space the amplitude of the resultant waveform at that point will be zero.
Path Difference
The difference in distance travelled by two waves from their sources to the point where they meet.
What makes Lasers the ideal piece of equipment to analyse diffraction and intensity patterns
Lasers are the ideal piece of equipment to analyse diffraction and intensity patterns because they form light that is:
Coherent (have a constant phase difference and frequency)
Monochromatic (have the same wavelength)
Safety Issues with Lasers
Lasers produce a very high-energy beam of light
This intense beam can cause permanent eye damage or even blindness
Lasers safety Precautions
Itβs important to use lasers safely and follow the guidelines:
* Do not look into laser
* Do not point the laser at others
* Avoid (accidental) reflections (e.g. by keeping experiement well below eye level)
* Display βlaser onβ warning light outside room
Two source interference (sound waves)
Two speakers will act as coherent sources if they are driven from the same signal generator (they will emit in phase at the same frequency). The diffraction patterns from the speakers overlap and the waves superpose. At positions where the path difference is an integer number of wavelengths, as in the diagram, the two waves will be in phase and maxima will be observed. At positions where the path difference is an odd multiple of half-wavelengths, the two waves will be in antiphase and minima will be observed.
Two source interference (microwaves)
Coherent microwave sources can be produced by driving two microwave emitters from the same source or by placing a pair of parallel slits (double slits) in front of one emitter. Microwave emitters produce polarised waves, so it is important to consider the orientation of the sources and the detector.
describe the interference pattern for 2 source interference monochromatic light
In the case that the slit is an infinitesimally thin point source of light, the interference pattern consists of evenly spaced light and dark fringes of equal intensity - faintly shown in diagram.
In the normal case that the slit is not an infinitesimally thin point source of light and has a measurable width, the interference pattern consists of evenly spaced light and dark fringes which decrease in intensity as you go further from the centre - highlighted in diagram
describe interfernce pattern for 2 source interfernce of white light
same as monochromatic light BUT
White central maximum, uniform width bright coloured side fringes with blue closest to centre and red furthest away.
describe interfernce pattern for 2 source interfernce of 2 colour light e.g. magenta
central magenta maxima - path difference of blue and red light is both 0 at this point
blue light has a shorter wavelngth thus a shorter path difference and will form as a maxima cloaser to the centre than red light
each blue maxima is one blue wavlength away from each other - same for red
eventually they would meet again forming another magenta
youngs double slit experiment
- used sunlight
- passed light through a filter so it was monochromatic
- a single slit was used to diffract the light to illuminate two slits
- as it is different paths of the same wave passing through both slits they act as a coherent source (constant phase diference)
Derivation of the double slit equation
There is a parallel line approximation - X1 and x2 are parallel
Developing Theories of EM Radiation
Isaac Newton (1672) - corpuscles
Christiaan Huygens (1678) - Wave Theory of Light
Thomas Young (1801) - double-slit experiment
James Clerk Maxwell (1862) - EM waves and the wave equation.
Albert Einstein (1905) - photoelectric effect
Later the scientific community came to understand that light behaves both like a wave and a particle.
This is known as wave-particle duality
Developing Theories of EM Radiation - Isaac Newton (1672)
Newton proposed that visible light is a stream of microscopic particles called corpuscles
However, these corpuscles could not explain interference or diffraction effects, therefore, the view of light as a wave was adopted instead
Developing Theories of EM Radiation - Christiaan Huygens (1678)
Huygens came up with the original Wave Theory of Light to explain the phenomena of diffraction and refraction
This theory describes light as a series of wavefronts on which every point is a source of waves that spread out and travel at the same speed as the source wave
These are known as Huygensβ wavelets
Developing Theories of EM Radiation - Thomas Young (1801)
Young devised the famous double-slit experiment
This provided experimental proof that light is a wave that can undergo constructive and destructive interference
Developing Theories of EM Radiation - James Clerk Maxwell (1862)
Maxwell showed that electric and magnetic fields obeyed the wave equation. This means that light was simply waves made up of electric and magnetic fields travelling perpendicular to one another
Later, Maxwell and Hertz discovered the full electromagnetic spectrum
Developing Theories of EM Radiation - Albert Einstein (1905)
Einstein discovered that light behaves as a particle, as demonstrated by the photoelectric effect
He described light in terms of packets of energy called photons
Later the scientific community came to understand that light behaves both like a wave and a particle
This is known as wave-particle duality
describe the diffraction pattern of monochomatic light through a single slit
Broad and bright central maximum, twice as wide as side maxima, intensity of maxima decreasing away from centre.
outer fringes of the same order are of the same width
A source of white light diffracted through a single slit will produce the following intensity pattern:
- Broad white central maximum,
- each subsidiary maxima are composed of a spectrum
- subsidiary maxima have violet nearest central maximum and red furthest from centre
- The non-central maxima are wider and less intense
- dark fringes are smaller (or not present)
Calculating w in single slit diffraction
The path difference between top and bottom of slit is
ΞπΏ = π sinβ‘π = ππ /π·
First minimum occurs when ΞπΏ=π
So, separation of minima given by
π= ππ· / π
Changes in Slit Width affect on single slit diffraction
If the slit was made narrower:
* The angle of diffraction is greater
* So, the waves spread out more beyond the slit
The intensity graph will show that:
* The intensity of the maxima decreases
* The width of the central maxima increases
* The spacing between fringes is wider
diffraction grating
A diffraction grating consists of a large number of very thin, equally spaced parallel slits carved into a glass plate at regular spacings distance d apart
Explain how light from the diffraction grating forms a maximum on the screen
Light from slits undergo diffraction and overlap
Path difference is a whole number of wavelengths
Arrive at screen in phase
Meet and undergo superposition
diffraction grating equation
The path difference between rays coming from adjacent lines is
ΞπΏ=π sinβ‘π
The rays will therefore all be in phase with one another when
π sinβ‘π=ππ
calculating line spacing - d
π= 10^(β3) / (lines per mm)
π=1/(lines per m)
Maximum Order of a diffraction grating
The largest order that can appear in a diffraction pattern is given by
π_max=π/π (rounded down)
The total number of bright spots that appear in the pattern is given by
π_spots=2π_max+1
Diffraction grating of monochromatic light
Narrow maxima of equal intensity that get further apart at higher orders away from the center
Diffraction grating of white light
Narrow, white central maximum. A spectrum at 1st order maximum with blue closest to centre and red furthest away. Broader, overlapping spectra at 2nd and higher orders
Uses of diffraction gratings
- Analysing spectra from stars, galaxies, etc. to determine composition, temperature etc.
- Measuring the wavelength of a laser
- Chemical analysis and identification (e.g absorption spectrum colorimetry)
Diffraction gratings role in X-ray crystallography
X-rays are directed at a thin crystal sheet which acts as a diffraction grating to form a diffraction pattern
This is because the wavelength of X-rays is similar in size to the gaps between the atoms
This diffraction pattern can be used to measure the atomic spacing in certain materials - d in equation
Refractive Index
The refractive index π of a material is defined to be given by:
π=π/π_π
where π is the speed of light in a vacuum 3.00Γ10^8 m s^(β1) and π_π is the speed of light in the material
e.g. in glass the speed of light is 2.00Γ10^8 m s^(β1) so it has a refractive index of 1.50.
Snellβs Law
When a light ray strikes the boundary between two media, it is partially reflected and partially transmitted
The reflected ray has the angle of incidence equal to angle of reflection
The refracted ray obeys Snellβs law
π_1 x sinβ‘π1 = π_2 x sinπ2
where π is angle between ray and normal line
Refraction
Refraction is:
The change in direction of a wave when it passes through a boundary between mediums of different density
This change of direction is caused by a change in the speed of different parts of the wavefront as they hit the boundary
medium definition in optics
used to describe a transparent material
How does light refract based on the intial and final medium
The more optically dense the new medium compared to the old one, the slower the waves travel and the smaller the angle of refraction - The light bends towards the normal.
The less optically dense the medium, the faster the waves travel and the larger the angle of refraction - The light bends away from the normal.
The angles of incidence and refraction are measured from the normal line.
This is drawn at 90Β° to the boundary between the two media
What happens to the speed, frequency and wavelength of light when it refracts
When a wave refracts, its speed and wavelength change, but its frequency remains the same
This is noticeable by the fact that the colour of the wave does not change
what happens when the light ray is incident on the boundary at 90Β°:
The wave passes straight through without direction
This is because the whole wavefront enters the boundary at the same time
Total Internal Reflection
If π_2 < π_1 (new medium is less dense than the old one) then there exists a critical angle given by
sinπ_π = π_2 / π_1
If π_1 > π_π, then it is impossible for a refracted ray be transmitted through the boundary, so the light is totally internally reflected.
When the angle of incidence = critical angle then:
Angle of refraction = 90Β°
The refracted ray is refracted along the boundary between the two materials
Fibre Optic Cables
An optical fibre is a thin piece of flexible glass, which light can travel down due to total internal reflection.
Uses of Fibre Optic Cables
Communications, such as telephone and internet transmission
Medical imaging, such as endoscopes
role of the Core in a fibreoptic cable
It propagates the wave/light by TIR as refractive index of core > cladding
role of the cladding in a fibreoptic cable
- Protect the thin core from damage and scratching
- Prevent signal degradation through light escaping the core, which can cause information from the signal to be lost
- It keeps the signals secure and maintains the original signal quality
- It keeps the core separate from other fibres preventing information crossover
pulse broadening
Where the pulses emerging from the fibre are longer than those entering
Pulse broadening is caused by modal and material dispersion
This can result in the merging of pulses, which distorts the information in the final pulse and increases the amplitude of the signal
Material Dispersion
When white light is used instead of monochromatic light inside an optical fibre it is separated into all the colours of the spectrum
Each wavelength of light travels at the same speed in a vacuum but at different speeds in a medium
Violet light has the shortest wavelength, so it travels the slowest in the fibre.
This means its angle of incidence on the fibre boundary is smallest compared to the other colours.
The angle of incidence is equal to the angle of reflection, so the angle of reflection is also smaller.
This means it takes longer for the violet colour to travel down the fibre because it undergoes more reflections
Modal Dispersion
Rays travelling at different angles inside the fibre travel different distances, and so take different times to reach the end of the fibre.
This is because each part of the wavefront has a different angle of incidence and consequently a different angle of reflection
So each part of the wavefront undergoes total internal reflection a different number of times
Hence, each part of the wavefront reaches the end of the fibre at a slightly different time
This leads to pulse broadening
How to reduce Modal Dispersion
Modal dispersion can be reduced by using cladding, which gives a large critical angle, so only rays close to the axis can travel. It can be eliminated entirely by making the fibre narrow enough that it becomes monomodal.
pulse absorbtion
The absorption of a signal in an optical fibre occurs when the fibre absorbs part of the signalβs energy
This reduces the amplitude of the signal, which can lead to a loss in the information transmitted
Reducing Pulse Absorption
Use an extremely transparent core
Use optical fibre repeaters so the pulse is regenerated before significant absorption has taken place
how to reduce pulse broadening
Use a core that is as narrow as possible to reduce the possible differences in the path length of the signal
Use of a monochromatic source so the speed of the pulse is constant
Use optical fibre repeaters so the pulse is regenerated before significant pulse broadening has taken place
Use a single-mode (monomodal) fibre, where only a single wavelength of light passes through the core, to reduce multipath modal dispersion
The diagram below shows light reflecting from the upper and lower surfaces of a transparent layer. Why will light with a wavelength of 356 nm (in the layer) will not be observed to be reflected from the transparent layer?
The path difference between A and B is half a wavelength
so A and B are 180Β° out of phase
so destructive intereference occurs.
When canβt the equation βw = Ξ»d / s used?
The equation is only valid if the fringe separation, w, is much less than the distance D from the slits to the screen.
If this criteria is not met you will need to use geometry.
What mistake is easily made with this question?
The angle of incidence is 55Β° not 35Β°
Always measure from the normal!
