waves Flashcards
progressive wave
A wave that transfers energy from one point to another without transferring the medium itself
A wave is caused by something making particles or fields (e.g. electric or magnetic fields) oscillate (or vibrate) at a source. These oscillations pass through the medium (or field) as the wave travels, carrying energy with it. A wave transfers this energy away from its source - so the source of the wave loses energy.
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.
Refraction
the wave changes direction as it enters a different medium. The change in direction is a result of the wave slowing down
or speeding up.
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 a particle in the wave from its equilibrium position
Properties of a Progressive Wave - Wavelength (λ)
Wavelength (λ) 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)
Frequency (f) is the number of complete oscillations per unit time. Measured in 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
The phase difference between two waves is a measure of how much a point or a wave is in front or behind another
This can be found from the relative positive of the crests or troughs of two different waves of the same frequency
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
Phase difference is measured in fractions of a wavelength, radians
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 × 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 ÷ 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 it’s travelling through (that’s why sound can’t travel in a vacuum).
Some types of earthquake shock waves are also longitudinal (P-waves).
How energy is transmitted through a longitudinal wave by:
The particles in the medium vibrating as they are given energy
The compressions cause the nearby particles to also vibrate with more energy
This produces a compression further along in the medium
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 360°, 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
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 — 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, 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 λ / 2, so the speed of sound c = fλ 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
When waves pass through an opening or around an obstacle they spread out to occupy areas that would otherwise be in shadow.
- 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 2π, 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)λ
where n is an integer i.e. 0.5λ, 1.5λ, 2.5λ,
the phase difference between the waves will be an odd multiple of π, so the waves arrive in antiphase and superpose to give a low amplitude wave – 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
It’s important to use lasers safely and follow the guidelines:
* Never look directly at a laser or its reflection
* Don’t shine the laser towards a person
* Don’t allow a laser beam to reflect from shiny surfaces into someone else’s eyes
* Wear laser safety goggles
* Place a ‘laser on’ warning light outside the room
* Stand behind the laser
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
symmetrical
highest amplitude in the middle
all maximas are of the same width
fringe spacing is constant
describe interfernce pattern for 2 source interfernce of white light
same as monochromatic light BUT
central maxima is white, other orders are full spectrums
eventually there would be another white maxima (in higher orders)
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 Huygens’ 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
central maxima twice the width as outer fringes
peak intensity of fringes decrease with distance 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:
The central maxima is equal in intensity to that of monochromatic light
The non-central maxima are wider and less intense
The fringe spacing between the maxima get smaller
The amount of red wavelengths in the pattern increases with increasing maxima, n increases from n = 1, 2, 3…
The amount of blue wavelengths decrease with increasing maxima
Changes in Wavelengths affect on single slit diffraction
When the wavelength passing through the gap is increased then the wave diffracts more
This increases the angle of diffraction of the waves as they pass through the slit
So the width of the bright maxima is also increased
Red light – which has the longest wavelength of visible light – will produce a diffraction pattern with wide fringes
Blue light – which has a much shorter wavelength – will produce a diffraction pattern with narrow fringes
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
