Waves Flashcards
What are progressive waves?
Wave which distribute energy from a point source to a surrounding area. They move energy in the form of vibrating particles or fields
What are mechanical waves?
Waves that are caused by a mechanical vibration or oscillation and require a medium to travel through such as air or water. These include sound waves, seismic waves and water waves
What are electromagnetic waves?
Waves that are caused by oscillations of electrons between different levels of energy and do not require a medium to propagate so they can travel through a vacuum. These include light waves, ultraviolet, infrared, radio waves, x-rays and microwaves
What are transverse waves?
Waves in which the direction of oscillation is perpendicular to the direction of travel. These include electromagnetic waves, some seismic waves (S type), water waves
What are longitudinal waves?
Waves in which the direction of oscillation is parallel to the direction of travel. These include sound waves, some seismic waves (P type)
What is the amplitude of a wave?
The maximum distance moved by a particle from its undisturbed position (halfway between the peak and the trough)
What is the wavelength of a wave?
The distance between successive peaks, or troughs, or any similar points on the wave
What is a complete cycle of oscillation?
The movement followed by a particle due to one wave
What is the frequency of a wave?
The number of complete cycles of oscillation that occur per second. Measured in Hz (1 Hz = 1 cycle per second)
What is the period of a wave?
The length of time taken for 1 complete cycle of oscillation
What equation links frequency and period?
T = 1/f
What is wave speed?
The wave speed is the speed of progression of the wave. It is the distance moved by a crest or any point on the waveform in one second
What is the phase of a wave?
The phase difference between 2 points n a wave is the fraction of a cycle by which one moves behind the other (expressed in degrees or radians)
Waves that are in phase are moving in the same direction at the same speed but are separated by a whole number of wavelengths.
Points that are separated by an odd number of half wavelengths are out of phase and waves that are out of phase by 180° are in antiphase
What is a wavefront?
A line joining all points of a wave that are in phase. The minimum distance between 2 points on a wave that oscillate in phase is equal to the wavelength. Wavefront is always perpendicular to wave direction
Reflection in light
The image and the object are equal distances from the mirror, the image is laterally inverted and the image is virtual/imaginary as no light is coming from it
Refraction in light
When light passes into another transparent material that is more optically dense then it slows down, causing it to bend towards the normal. The more dense the material, the more it slows
Refractive index
n = sin(i) / sin (r) = c vacuum / c material = λ vacuum / λ material
Refractive index is always greater than 1 and if light is travelling from material to vacuum then the equation must be inverted
Air can be treated as a vacuum
Diffraction
A wave will diffract as it goes through a gap or past an obstacle. Wavelength is unchanged before and after passing through the gaps. The closer the gap width is to the wavelength the more the wave will diffract
What is interference?
When 2 waves meet/cross they interfere and combine to give a resultant wave of a different amplitude. The pattern produced by the crossing of waves is called an interference pattern.
What is the principle of superposition?
The displacement of the point where the waves meet is equal to the vector sum of the displacements of each of the waves at that point
What is needed to form a ‘stable’ interference pattern?
They must be of the same frequency otherwise the interference pattern will be constantly changing
What is coherence?
Coherent waves are one with a constant phase difference (but do not have to be in phase) and will have the same frequency and wavelength. They are usually produced by the same source
What is destructive interference?
If 2 waves of the same type and frequency coincide so that a crest crosses a trough then the amplitudes completely cancel out. This is destructive interference and there will be no waves if the amplitudes are the same. This is a minima in light.
What is constructive interference?
If 2 waves of the same type and frequency combine so that 2 crests or 2 troughs coincide then there is constructive interference and the resultant amplitude is the sum of the separate amplitudes, and if the 2 initial amplitudes are equal then the amplitude of the resultant wave is double that of the original wave. This is a maxima in light.
Explanation of the observations in a ripple tank when there are waves produced using either 2 sources or 1 source through 2 gaps
There will be areas of flat water where destructive interference has occurred (waves have met in antiphase) and there is 0 amplitude.
Where the waves are double the height then there has been constructive interference where the waves have met in phase.
What is the path length difference between central maxima and the next maxima?
λ
What is the path length difference between the central maxima and the first minima?
λ / 2
Young’s double slit interference pattern (light)
At the centre there is superposition and constructive interference so a maxima is formed (waves meet in phase and are coherent as they are from one source) and their path length difference is 0
At the first minima there is destructive interference so a minima is formed (waves meet in antiphase and the path length difference is λ /2
If path length difference is nλ then there is constructive interference and a bright spot is formed
If path length difference is (n + 0.5)λ then there is destructive interference and a dark spot is formed
The effect of colour on fringe spacing
From a monochromatic source of light the fringes appear as one colour corresponding to the chosen wavelength (e.g. if λ = 700nm then they are red)
For a white light source, the central fringe is white and the other fringes are tinged with colour due to the different fringe spacings that occur because of the different wavelengths of the colours. The furthest colour is red as it has the longest wavelength and the first bright fringe is blue as it has the shortest wavelengths
Single slit diffraction (light)
Huygens wavelet idea supposes that each point on the wave emits secondary waves which form a new wavefront. Each section of the wave then spreads out beyond the slit and all points on the section contribute to the intensity. At a dark fringe then all the contributions cancel out.
The narrower the slit the greater the diffraction and the longer the wavelength the greater the diffraction
Single slit diffraction intensity distribution
High intensity central maxima with width double that of the secondary maxima. Intensity of peaks further out is much lower as only some sources interfere constructively.
In the fringe pattern there is a block in the centre, a block half the width corresponding to the next outermost peak of the intensity distribution and a block half the width of that for the next outermost peak
Intensity for double slit diffraction
The ‘ideal’ double slit intensity should be peaks of the same heights and widths if diffraction effects were neglected but the ‘true’ intensity has peaks of equal widths but the amplitudes decrease as it goes outwards as the ‘true’ intensity is a combination of single slit and double slit interference effects.
What is diffraction grating?
It is a useful tool for studying light and objects that emit and absorb it as it has many slits per millimetre.
When monochromatic light is sent through the slits then it forms narrow interference fringes that can be analysed to determine the wavelength of light (using nλ = d sinθ). When white light is used then it gives a mini-spectrum of colours in each diffracted beam with red light being diffracted the most as it has the longest wavelength and blue with the least as it is the shortest.
Explanation of nλ = d sinθ
θ = angle between original direction of waves and a bright spot λ = wavelength of light n = order of fringe d = spacing between slits on grating (if there are 300 gaps per mm then there are 300x10^3 gaps per metre and so d = 1 / 300x10^3)
Use of different laser beams for different types of disc (CD, DVD etc)
Different coloured laser beams will be used as each disc has different sized bumps depending on how much information they store and so the different lasers need to have different wavelengths
What is the basic structure of the reflecting part of a CD?
The surface of a CD is made up of pits and plateaus and it is covered in aluminium.
When the laser hits a plateau then it is reflected and interferes constructively and the output signal is high, corresponding to a 1 (binary code)
When it is reflected from the edge of a plateau then there will be destructive interference, as one part of the beam travels a half wavelength further than the other, causing a low output signal, corresponding to a 0
As the CD continues to move, the laser beam will be reflected from a pit, then from the edge of a pit, then from another plateau. When reflected from a flat surface, constructive interference always occurs and when reflected from the edge then destructive interference always occurs
What is a stationary/standing wave?
They are set up as a result of the superposition of 2 identical waves (same amplitude and frequency) travelling at the same speed but in opposite directions. They frequently occur when a wave reflects back from a surface and interferes with itself.
Wave peaks do not move along (they are stationary) so wave energy stays in the same position and is not transported through a medium.
In order for a standing wave to be set up then the distance between the source of vibration and reflecting surface must be a complete number of half wavelengths
Nodes and antinodes
The part of the standing wave where the amplitude is 0 are called nodes
Halfway between the nodes where the amplitude is at a maximum there are antinodes.
Length = nλ / 2 (whole number of half wavelengths)
Distance between nodes = λ / 2
Distance between antinodes = λ /2
Calculating wavelength of a microwave (using standing waves)
Set up a microwave emitter and a metal plate so that microwaves are reflected and use a microwave detector to work out the positions of the nodes and antinodes. Measure the distance between 9 nodes (for example) and then distance = 8 x λ/2 (λ/2 = distance between nodes) then λ = d/4 -> v = fλ = f x d/4
Reflecting sound waves
The transmitted wave gets smaller in amplitude the further it travels, so a proper standing wave is not set up, but the point at which the reflected and emitted waves meet are almost at the same amplitudes so cancellation is possible. The amplitudes can be measured using a microphone and an oscilloscope
Standing waves in musical instruments - resonance
When standing waves are set up in the medium that is vibrating it is essentially in resonance (resonating at its fundamental/natural frequency or at a harmonic of that frequency)
Many musical instruments produce sound waves by setting up a standing wave either in a column of air or in a string, and the design of musical instruments is built around optimising the patterns of resonance
Harmonics in stringed instruments
Fundamental frequency / first harmonic (n=1) - 2 nodes at either end and 1 antinode in the middle Second harmonic (n=2) - 3 nodes, at the beginning, middle and end, and an antinode in between them Third harmonic (n=3) - 4 nodes with equal spacing, 3 antinodes in between them This pattern continues
Harmonics in wind instruments - air column closed at 1 end
Fundamental frequency / first harmonic - node at closed end, antinode at open end. λ = 4L
Second harmonic - node at closed end, then antinode, then node, then antinode at open end. λ = 4/3 L
Third harmonic - 3 nodes (with 1 at closed end) and 3 antinodes (1 at open end). λ = 4/5 L
Harmonics in wind instruments - air column closed at both ends
Fundamental frequency / first harmonic - antinode at each open end, node in middle. λ = 2L
Second harmonic - 3 antinodes (2 at each end and 1 at centre) with nodes in between them. λ = L
Third harmonic - 4 antinodes (2 at each end) and nodes in between. λ = 2/3 L
Standing waves in string or wire
The speed of wave travel in a medium depends on the physical properties of that medium (e.g. nature of bonding), and for a wave on a string or wire the wave speed depends on the tension in the wire and the mass of the wire
Wave speed is given by v = √ (tension (T) / mass per unit length (μ))
For a wire of mass m (kg) and length (l) then μ = m / l so v = fλ
Derive the formula for frequency of a standing wave in a wire
v = fλ, v = √(T / μ) f = √(T/M) / λ = √(T/M/L) / λ = √(TL/M) / λ ------- f ∝ √T f ∝ 1/√L f ∝ 1/√m
Snell’s law
Snell’s law relates the refractive indexes of 2 media to the change in direction that a light ray takes when it crosses the boundary between them
v1 / v2 = sinθ2 / sinθ1
= 1n2 = sinθ1 / sinθ2
= va / v (speed of light in air / speed of light in material
General formula: n1 sinθ1 = n2 sinθ2
Frequency does not change during refraction so fλa / fλm = λa / λm
Refraction (not in light)
Occurs for all types of waves, for example, sound waves can be refracted and so deviated as they pass from warm air to cold air, water waves when they move between deep and shallow water and in ultrasound when it moves between denser and less dense tissue
Derive the general formula for Snell’s Law
n1 = va / v1 , n2 = va / v2
n1 / n2 = sin θ2 / sin θ1(n1 / n2 = 1n2)
n1 sinθ1 = n2 sinθ2
Total internal reflection
When light passes at small angles of incidence from an optically denser to a less optically dense material then there is a strong refracted ray and a weak ray reflected in the denser medium.
At certain angles of incidence called the critical angle (C) the angle of refraction is 90° (from normal)
For angles greater than C all incident light is reflected and there is total internal reflection
Derive the formula for critical angle from Snell’s Law
n1 sinθ1 = n2 sinθ2
n1 = refractive index of glass (for example), n2 = refractive index of air = 1
θ1 = critical angle, θ2 = 90°
n1 / n2 = sin θ2 / sin θ1 = sin90 / sin θc
n1 = 1 / sin θc
sinC = 1 / n
How can a 45-45-90 (right angled triangle prism) be used to reflect light through
a) 90°
b) 180°
a) Shine light against the hypotenuse of the triangle, and the angle of incidence and refraction are 45°
b) Shine light against the hypotenuse of 1 (same as to reflect 90°) then add another prism that is a 90° rotation of the first one and the light is reflected another 90°
Use of total internal reflection in fibre optics
In thin fibres, the angle of incidence is always greater than the critical angle, so light is always reflected inside the fibre until the end. This is used in cable TV and in medicine for instruments such as bronchoscope
Dispersion
When white light is passed through a prism it is separated into its component colours. Red has the biggest wavelength so it has the largest θ2 (angle from normal inside prism) and is deviated the least. Violet has the greatest θ2 and so is deviated the most.
The addition of a further prism (flipped) can recombine the light from its component colours into white light
Derive a formula that shows the link between wavelength and deviation using equations for refractive index
n1 sinθ1 = n2 sinθ2
n2 = n = speed of light in air / speed of light in glass = c /v = c / fλ
sinθ1 = c sinθ2 / fλ
sinθ2 = fλ sinθ1 / c
Frequency and speed of light are constant, so sinθ2 ∝ λ , so the bigger the wavelength, the less deviated the light
What is a lens?
A lens is an object made of a clear material that has a curved face so that it changes the light by refraction, forming an image. There are converging lenses and diverging lenses
Converging lenses
A converging lens is convex. Incident rays which travel parallel to the principal axis will refract through the lens and converge to a point. The focal point of a converging lens is the point at which the rays converge/where they focus. The focal length of a converging lens is the distance from the centre of the lens to the focal point. Converging lenses produce a real image until it becomes a magnifying glass.
Diverging lenses
A diverging lens is concave. Incident rays travelling parallel to the principal axis will refract through the lens and diverge, never intersecting. The focal point of a diverging lens is the point at which parallel rays appear to diverge. Diverging lenses ALWAYS produce a virtual image.
Properties of lenses
Magnification is given by size of image / size of object
Focal length is given the symbol f (in metres)
Power is given by 1 / focal length
Power is measured in dioptres (D). The power of a converging lens is positive and the power of a diverging lens is negative
If lenses are placed one after another in combination, total power is given by P total = P1 + P2 + P3 …
A real image…
Can be shown on a screen, the other side of the lens to the object
A virtual image…
Cannot be shown on a screen and is the same side of the lens as the object
Image produced by a convex lens
Real, inverted and larger than the object
Image produced by a concave lens
Virtual, upright and smaller than the object
How to draw a ray diagram for a convex/converging lens
Draw:
- A ray travelling parallel to the principal axis which is refracted through the focal point
- A ray travelling through the centre of the lens which is undeviated
- A ray travelling from the focal point which is refracted parallel to the principal axis
How to draw a ray diagram for a concave/diverging lens
Draw:
- A ray travelling parallel to the principal axis that is refracted in such a way that it appears to come from the focal point (bends away from lens and if continued with a dotted line back towards the side of the lens that the object is then it goes through the focal point)
- A ray travelling through the centre of the lens which is undeviated
- A ray travelling towards the focal point (on the opposite side of the lens to the object) which is refracted parallel to the principal axis (if this original diagonal line is continued then it would pass through the focal point on the opposite side of the lens)
What does the image produced by a convex lens look like if the object is further than 2F?
The image is smaller than the object
The ray diagram follows the same rules
What does the image produced by a convex lens look like if the object is between F and 2F?
The image is bigger than the object
The ray diagram follows the same rules
What does the image produced by a convex lens look like if the object is closer than F?
A virtual image > 1 M
The ray diagram shows a ray passing diagonally through focal point on the opposite side of the lens to the object. and a ray diagonally passing over the object. The 2 rays converge at a point on the same side of the lens as the object
The lens formula
1/f = 1/u + 1/v
1 / focal length (m) = 1 / object distance (m) + 1 / image distance
The sign indicates whether an image is real or virtual, positive indicating a real image, negative indicating a virtual imahe
If a diverging lens is used then the focal length has a negative value
Experimental investigation of lens formula
From left to right of a diagram of apparatus: lamp, object, lens, screen. All on an optical rail.
Move the position of the object around and measure u, Then move the screen until the object appears in focus or is as clear as possible, then measure v
A graph of 1/v against 1/u can be plotted and would have a negative gradient, with the y intercept representing 1/f
Polarisation
Transverse waves can oscillate in any plane, and polarisation is the process by which the electromagnetic oscillations are made to occur in one plane only. This is done by passing the waves through a ‘grid’, which only allow waves moving in a certain way to fit through. Polarisation can also by achieved when waves are only ever created in one plane, like in a laser. Light reflecting off water is polarised.
Longitudinal waves cannot be polarised as there is no plane of vibration at right angles to direction of travel
Experiment to show polarisation of light waves
Set up 2 polaroids in such a way that allows bright light to be seen, then rotate the second filter by 90°. If the light fades to dark, then it shows it is polarised.
With 1 filter than oscillations occur in 1 plane which includes direction of wave and direction of propagation. After the first filter, light is vertically polarised (for example) and when the 2nd filter is aligned with the first then the same component can pass through, so the light observed is bright. If the 2nd filter is rotated by 90°, then there is no component of light polarised in that direction, so no light can pass through
Experiment to show polarisation of microwaves
Set up a microwave transmitter, then a horizontal metal grill, then a microwave receiver. The microwaves produced are polarised as they are caused by a vibrating electron (vertical), and the microwave receiver will display a maximum signal when the grill is horizontal and microwaves are vertical. If the grill is rotated by 90° then the microwaves are absorbed by the metal and the receiver will show a 0 signal
What is echolocation?
Acoustic/echolocation is the science of using sound to determine the distance and direction of an object and can take place in gases, liquids and solids.
Active acoustic location involves the creation of sound in order to produce an echo, which is then analysed to determine the location of the object in question (used by animals like bats and dolphins to find prey and in ultrasound sonography)
Passive acoustic location involves the detection sound or vibration created by the by the object being detected which is then analysed to then determine the location of the object in question (used by submarines to detect other submarines)
Experiments using echoes
It can be determined by timing the period between emitting a sound and receiving its echo from a surface a measured distance away.
The distance of a surface may be measured by measuring the time for the reflection to be received and knowing the speed of sound through the medium, which is the principal behind echo location. Distance is measured using d = v x t/2
Pulse echo detection
Uses short bursts of usually very high frequency sound to detect distances and construct an image of the object(s) being scanned. The technique is used in many applications from sonar on ships and submarines, to air traffic control and medical imaging.
Pulse echo resolution
Resolution is determined by the wavelength of the sound and by the length of the pulse sent.
- the smallest detail that can be distinguished will be the same size as the wavelength. The smaller the wavelength, the finer the detail that can be distinguishes
- λ is usually between 0.075 and 1.5 mm
- the shorter the wavelength, the sooner a wave pulse will be absorbed
- with pulse echo imaging the resolution will be half the length of a pulse - all the pulse must return before the next one is sent or if there are 2 reflections then the returning pulses must not overlap or they cannot be distinguished
- the smallest distance must be greater than half the wavelength
- pulse length = speed x time
- pulse repetition frequency determines the the maximum speed that can be determined in Doppler ultrasound. Higher PRF means higher speeds can be detected but limits the range of detection.
- the repetition period should be greater than the echo time so all the echoes return before the next pulse is sent.
What is the frequency of ultrasound?
Sound with frequency greater than 20,000Hz - above the audible range of human hearing
How does ultrasonography (using ultrasound as a diagnostic imaging technique) work?
- It uses a probe containing one or more acoustic tranducers to send pulses of sound into a material
- Whenever a sound wave encounters a material with a different density, part of the sound wave is reflected back to the probe and is detected as an echo
- The time it takes for the echo to travel back to the probe is measured and used to calculate the depth of the tissue interface causing the echo
- The greater the difference between densities, the larger the echo
- If the pulse hits gases or solids, the density difference is so great that most of the acoustic energy is reflected and it becomes impossible to see deeper
How can the speed of a moving object be measured using ultrasound?
If a pulse is reflected from a moving object then the reflected sound will undergo a change in frequency when compared to the emitted sound because of the Doppler effect - if Doppler shift is measured then the speed of the moving object can be determined
