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.
Diffraction
the wave spreads out as it passes through a gap or round an obstacle. E.g. you can hear sound from round a corner.
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, degrees or 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 at right angles to the direction of energy propagation (transfer).
All electromagnetic waves are transverse. They travel as oscillating magnetic and electric fields.
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 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
This only allows oscillations in a certain plane to be transmitted
Diagram A shows that only unpolarised waves can be polarised
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
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
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
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
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
Superposition of waves
Superposition happens when two or more waves pass through each other.
At the instant that waves cross, the displacements due to each wave combine.
Then each wave continues on its way. You can see this if two pulses are sent simultaneously from each end of a rope.
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.
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
Total destructive interference
If two waves with equal and opposite displacements meet (e.g. a crest and a trough with equal magnitudes), they cancel each other out completely.
This is called total destructive interference
2 points on a wave which are in phase
Two points on a wave are in phase if they are both at the same point in the wave cycle (the same phase — see p.69). Points in phase have the same displacement and velocity.
In Figure 5, points A and B are in phase; points A and C are out of phase; and points A and D are exactly out of phase.
Measuring phase difference between different points on a wave
It’s mathematically handy to show one complete cycle of a wave as an angle of 360° (2pi radians). The phase difference of two points on a wave is the difference in their positions in a wave’s cycle, measured in degrees, radians or fractions of a cycle. Two points with a phase difference of zero or a multiple of 360° (i.e. a full cycle) are in phase. Points with a phase difference of odd-number multiples of 180° ( radians, or half a cycle) are exactly out of phase.
What is a stationary wave?
A stationary (standing) wave is the superposition of two progressive waves with the same trequency (or wavelength) and amplitude, moving in opposite directions. Unlike progressive waves, no energy is transmitted by a stationary wave.
You can see how stationary waves are formed by considering two waves moving in opposite directions on a graph of displacement against position
Nodes & Antinodes on stationary waves
A stationary wave is made up nodes and antinodes
Nodes are regions where there is no vibration
Antinodes are regions where the vibrations are at their maximum amplitude
The nodes and antinodes do not move along the string
Nodes are fixed and antinodes only move in the vertical direction
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
First harmonic / fundamental frequency
This stationary wave is vibrating at its lowest possible resonant frequency, called the first harmonic - see Figures 3-6. It has one “loop” with a node at each end. One half wavelength fits onto the string, and so the wavelength is double the length of the string.
Second harmonic
It has twice the frequency of the first harmonic. There are two “loops” with a node in the middle and one at each end. Two half wavelengths fit on the string, so the wavelength is the length of the string.
formula for frequency of harmonics
The frequencies can be calculated from the string length and wave equation
For a string of length L, the wavelength of the lowest harmonic is 2L
This is because there is only one loop of the stationary wave, which is a half wavelength
Therefore, the frequency is equal to:
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.
The speed of a wave travelling along a string with two fixed ends is given by:
combined eqn for frequency of the first harmonic
equation for mass per unit length
equation for string tension
