Waves Flashcards
What are progressive waves?
A wave that transfers energy from one point to another without transferring the medium itself
Properties of a progressive wave
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
Amplitude (A) is the maximum displacement of a particle in the wave from its equilibrium position
Wavelength (λ) is the distance between points on successive oscillations of the wave that are in phase
These are all measured in metres (m)
What is phase difference a measure of
how much a point or a wave is in front or behind another
What is polarisation
Particle oscillations occur in only one of the directions perpendicular to the direction of wave propagation
Why can polarisation only occur in transverse waves?
because transverse waves oscillate in any plane perpendicular to the propagation direction
What does it mean when transverse waves are polarised
Vibrations are restricted to one direction
These vibrations are still perpendicular to the direction of propagation / energy transfer
Applications of polarisers: Polaroid sunglasses
Polaroid sunglasses are glasses containing lens with polarising filters with transmission axes that are vertically oriented
- the glasses do not allow any horizontally polarised light to pass through
When light is reflected from a reflective surface 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 sunglasses are useful in reducing the glare on the surface of the water (or any reflective surface) as the partially-polarised light will be eliminated by the polarising filter
So objects under water surface are viewed more clearly
Applications of polarisations: Polaroid photography
Polarising 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 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
Applications of polarisation : Polarisation of radio & microwave signals
Radio and television services are broadcast either horizontally-polarised or vertically-polarised
Therefore, the reception aerial needs to be mounted flat (horizontal), or on its side (vertical),
The particular orientation of an aerial will depend on the transmitter it is pointing towards and the polarity of the services being broadcast
How are standing waves produced
by the superposition of two waves of the same frequency and amplitude travelling in opposite directions
This is usually achieved by a travelling wave and its reflection
The superposition produces a wave pattern where the peaks and troughs do not move
Do stationary waves store energy or not
Yes, unlike progressive waves which transfer energy
What are nodes
Regions where there is no vibration
What are anti nodes?
Regions where the vibrations are at their maximum amplitude
When are points in phase or out of phase
Points between nodes are in phase with each other
Points that have an odd number of nodes between them are out of phase
Points that have an even number of nodes between them are in phase
State the principle of superposition
When two or more waves with the same frequency arrive at a point, the resultant displacement is the sum of the displacements of each wave
Describe superposing IN PHASE
causes constructive interference.
The peaks and troughs line up on both waves and the resultant wave has double the amplitude
Describe superposing in ANTI-PHASE
Causing destructive interference.
The peaks on one wave line up with the troughs of the other. The resultant wave has no amplitude
When is a stationary wave formed
Two waves travelling in opposite directions along the same line with the same frequency superpose
Examples of stationary waves: stretched string
Vibrations caused by stationary waves on a stretched string produce sound
This is how stringed instruments, such as guitars or violins, work
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, standing waves with different numbers of minima (nodes) and maxima (antinodes) form
Examples of stationary waves: microwaves
A microwave source is placed in line with a reflecting plate and a small detector between the two
The reflector can be moved to and from the source to vary the stationary wave pattern formed
By moving the detector, it can pick up the minima (nodes) and maxima (antinodes) of the stationary wave pattern
Examples of stationary waves: sound waves
Sound waves can be produced as a result of the formation of stationary waves inside an air column
This is how musical instruments, such as clarinets and organs, work
This can be demonstrated by placing a fine powder inside the air column and a loudspeaker at the open end
At certain frequencies, the powder forms evenly spaced heaps along the tube, showing where there is zero disturbance as a result of the nodes of the stationary wave
In order to produce a stationary wave, there must be a minima (node) at one end and a maxima (antinode) at the end with the loudspeaker
What are harmonics
Different wave patterns
What do harmonics depend on
on the frequency of the vibration and the situation in which they are created
Harmonics on a string
Frequency formula
Required Practical: Investigating Stationary Waves
Aims
The overall aim of the experiment is to measure how the frequency of the first harmonic is affected by changing one of the following variables:
The length of the string
The tension in the string
Strings with different values of mass per unit length
Required Practical: Investigating Stationary Waves
Variables
Independent variable = either length, tension, or mass per unit length
Dependent variable = frequency of the first harmonic
Control variables
If length is varied = same masses attached (tension), same string (mass per unit length)
If tension is varied = same length of the string, same string (mass per unit length)
If mass per unit length is varied = same masses attached (tension), same length of the string
Required Practical: Investigating Stationary Waves
Method
- Set up the apparatus by attaching one end of the string to the vibration generator and pass the other end over the bench pulley and attach the mass hanger
- Adjust the position of the bridge so that the length L is measured from the vibration generator to the bridge using a metre ruler
- Turn on the signal generator to set the string oscillating
- Increase the frequency of the vibration generator until the first harmonic is observed and read the frequency that this occurs at
- Repeat the procedure with different lengths
Repeat the frequency readings at least two more times and take the average of these measurements - Measure the tension in the string using T = mg
Where m is the amount of mass attached to the string and g is the gravitational field strength on Earth (9.81 N kg–1) - Measure the mass per unit length of the string μ = mass of string ÷ length of string
- Simply take a known length of the string (1 m is ideal) and measure its mass on a balance
Required Practical: Investigating Stationary Waves
Systematic errors
An oscilloscope can be used to verify the signal generator’s readings
The signal generator should be left for about 20 minutes to stabilise
The measurements would have a greater resolution if the length used is as large as possible, or as many half-wavelengths as possible
This means measurements should span a suitable range, for example, 20 cm intervals over at least 1.0 m
Required Practical: Investigating Stationary Waves
Random errors
The sharpness of resonance leads to the biggest problem in deciding when the first harmonic is achieved
This can be resolved by adjusting the frequency while looking closely at a node. This is a technique to gain the largest response
Looking at the amplitude is likely to be less reliable since the wave will be moving very fast
When taking repeat measurements of the frequency, the best procedure is as follows:
Determine the frequency of the first harmonic when the largest vibration is observed and note down the frequency at this point
Increase the frequency and then gradually reduce it until the first harmonic is observed again and note down the frequency of this
If taking three repeat readings, repeat this procedure again
Average the three readings and move onto the next measurement
When does interference occur
when waves overlap and their resultant displacement is the sum of the displacement of each wave
What is coherence
At points where the two waves are neither in phase nor in antiphase, the resultant amplitude is somewhere in between the two extremes
When are waves said to be coherent
If they have:
The same frequency
A constant phase difference
What is the importance of coherence
Coherence is vital in order to produce an observable, or hearable, interference pattern
Laser light is an example of a coherent light source, whereas filament lamps produce incoherent light waves
When coherent sound waves are in phase, the sound is louder because of constructive interference
Define path difference
The difference in distance travelled by two waves from their sources to the point where they meet
What is constructive interference in the screen
Bright fringes
- the highest intensity is in the middle
What is destructive interference in the screen
Dark fringes
- these have zero intensity
For two-source interference fringes to be observed, the sources of the wave must be…
Coherent (constant phase difference)
Monochromatic (single wavelength)
What will the difference in wavelengths be for constructive interference
an integer number of whole wavelengths
What will be the number of wavelengths for destructive interference (or minima)
an integer number of whole wavelengths plus a half wavelength
What does young’s double slit experiment demonstrate
how light waves can produce an interference pattern
Describe young’s double slit experiment
When a monochromatic light source is placed behind a single slit, the light is diffracted producing two light sources at the double slits A and B
Since both light sources originate from the same primary source, they are coherent and will therefore create an observable interference pattern
Both diffracted light from the double slits create an interference pattern made up of bright and dark fringes
3.3.5 Required Practical: Young’s Slit Experiment & Diffraction Gratings
Variables
Independent variable = Distance between the slits and the screen, D
Dependent variable = Fringe width, w
Control variables
Laser wavelength, λ
Slit separation, s
3.3.5 Required Practical: Young’s Slit Experiment & Diffraction Gratings
Aim
to investigate the relationship between the distance between the slits and the screen, D, and the fringe width, w
3.3.5 Required Practical: Young’s Slit Experiment & Diffraction Gratings
Method
- Set up the apparatus by fixing the laser and the slits to a retort stand and place the screen so that D is 0.5 m, measured using the metre ruler
- Darken the room and turn on the laser
- Measure from the central fringe across many fringes using the vernier callipers and divide by the number of fringe widths to find the fringe width, w
- Increase the distance D by 0.1 m and repeat the procedure, increasing it by 0.1 m each time up to around 1.5 m
- Repeat the experiment twice more and calculate and record the mean fringe width w for each distance D
Interference by a Diffraction Grating practical aim
s to calculate the wavelength of the laser light using a diffraction grating
Interference by a Diffraction Grating practical variables
Independent variable = Distance between maxima, h
Dependent variable = The angle between the normal and each order, θn (where n = 1, 2, 3 etc)
Control variables
Distance between the slits and the screen, D
Laser wavelength λ
Slit separation, d
Interference by a Diffraction Grating practical
Method
- Place the laser on a retort stand and the diffraction grating in front of it
- Use a set square to ensure the beam passes through the grating at normal incidence and meets the screen perpendicularly
- Set the distance D between the grating and the screen to be 1.0 m using a metre ruler
- Darken the room and turn on the laser
Identify the zero-order maximum (the central beam) - Measure the distance h to the nearest two first-order maxima (i.e. n = 1, n = 2) using a vernier calliper
- Calculate the mean of these two values
Measure distance h for increasing orders
Repeat with a diffraction grating with a different number of slits per mm
Diffraction grating equation
nλ = d sin θ
what is diffraction
the spreading out of waves when they pass an obstruction
This obstruction is typically a narrow slit known as an aperture
What are the features of the single slit diffraction pattern
A central maximum with a high intensity
Subsidiary maxima equally spaced, successively smaller in intensity and half the width of the central maximum
What is a diffraction grating
a plate on which there is a very large number of parallel, identical, close-spaced slits
What happens when monochromatic light is incident on a grating
a pattern of narrow bright fringes is produced on a screen
Diffraction grating equation
How to calculate angular separation (diffraction grating)
The angular separation of each maxima is calculated by rearranging the grating equation to make θ the subject
The angle θ is taken from the centre meaning the higher orders are at greater angles
The angular separation between two angles is found by subtracting the smaller angle from the larger one
The angular separation between the first and second maxima n1 and n2 is θ2 – θ1
What are diffraction gratings useful for
separating light of different wavelengths with high resolution
What are diffraction gratings used in spectrometers to do
Analyse light from stars
Analyse the composition of a star
Chemical analysis
Measure red shift / rotation of stars
Measure the wavelength / frequency of light from a star
Observe the spectra of materials
Analyse the absorption / emission spectra in stars
What do diffraction gratings do 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
What are the only properties that change during refraction
speed and wavelength – the frequency of waves does not change
How to calculate refracting index
C = the speed of light in a vacuum m/s
Ces - the speed of light in a substance m/s
What is snells law
Snell’s law relates the angle of incidence to the angle of refraction, it is given by:
n1 sin θ1 = n2 sin θ2
Where:
n1 = the refractive index of material 1
n2 = the refractive index of material 2
θ1 = the angle of incidence of the ray in material 1
θ2 = the angle of refraction of the ray in material 2
Critical angle formula
When does total internal reflection occur
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 at the boundary n2
What are the two conditions for total internal reflection
The angle of incidence > the critical angle
The refractive index n1 is greater than the refractive index n2
What are three main components that make up optical fibres
An optically dense core, such as plastic or glass
A lower optical density cladding surrounding the core
An outer sheath
Since the refractive index of the core is more than the refractive index of the cladding, this allows TIR to occur
ncladding < ncore
What is importance of outer sheath in optic fibres
Prevents physical damage to the fibre
Strengthens the fibre
Protects the fibre from the outside from scratches
What is importance of cladding in optic fibres
It protects the core from damage
It prevents signal degradation through light escaping the core, which can cause information from the signal to be lost
It keeps signals secure and maintains the quality of the original signal
It prevents scratching of the core
It keeps the core away from adjacent fibre cores hence preventing crossover of information to other fibres
It provides the fibre with strength and prevents breakage given that the core needs to be very thin
Pulse broadening an absorption
When does absorption occur
Part of the signal’s energy is absorbed by the fibre
The signal is attenuated by the core
This reduces the amplitude of the signal, which can lead to a loss of information
Pulse broadening an absorption
What is pulse broadening caused by
modal and material dispersion
The consequence of pulse broadening is that different pulses could merge, resulting in a completely distorted final pulse
Reducing Pulse Broadening & Absorption
To reduce absorption:
Use a core which is extremely transparent
Use of optical fibre repeaters so that the pulse is regenerated before significant absorption has taken place
Reducing Pulse Broadening & Absorption
To reduce pulse broadening:
Make the core as narrow as possible to reduce the possible differences in path length of the signal
Use of a monochromatic source so the speed of the pulse is constant
Use of optical fibre repeaters so that the pulse is regenerated before significant pulse broadening has taken place
Use of single-mode fibre to reduce multipath modal dispersion
Role of the single slit
(The single slit makes) the waves from the light source coherent / identical / in phase (before they hit the double slit)
Role of the single slit
(The single slit makes) the waves from the light source coherent / identical / in phase (before they hit the double slit)
Explain why coherent light is required
Coherent light is needed to observe clear interference fringes
OR
The waves (from the double slit) must have a constant phase difference to observe clear interference fringes
Explain the formation of the fringes seen on the screen
Interference fringes are formed [1 mark]
When light from the two slits overlap/superpose [1 mark]
The light from the two slits is coherent [1 mark]
The bright/blue fringes are formed where light from the two slits interfere constructively/crest meets crest/reinforces [1 mark]
The dark fringes are formed where light from the two slits interfere destructively/crest meets trough/cancels [1 mark]
Constructive interference/reinforcement occurs when light waves are in phase/phase difference is a whole number of wavelengths [1 mark]
OR
Destructive interference/cancellation occurs when light waves are out of phase of 180°/in anti-phase/phase difference is an odd number of half wavelengths [1 mark]
