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Chapter 6: Wave Behaviour
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- 16.1; SUPERPOSITION OF WAVES.
- 2What does the principle of superposition state that?When 2 or more waves superpose:
resultant displacement at instant and position =
Sum of individual displacements at same instant and position. - 3What does a displacement-displacement diagram show?Snapshot of a wave at a single instant in time.
- 4What does a displacement-time diagram show?How the displacement of a point along a wave changes over time.
- 5What is the amplitude?The maximum displacement of the wave from the equilibrium position (where y=0)
- 6What is the time period?The time a point on a wave takes to return to the same position in the cycle (moving in the same direction).
-Time for one oscillation - 7What can you use to measure the time period of a wave?An oscilloscope.
- 8How do you find the frequency from this value?Frequency = 1/ Time Period.
F=1/T - 9What does phase describe?The stage in a wave cycle.
- 10When are 2 points in phase?When they are the same stage in the cycle at the same instant..
- 11What is the phase difference of 2 waves in phase? Why?No phase difference, because in same position at same instant.
- 12When are 2 waves in antiphase?When they are in exactly opposite positions at the same instant.
- 13What are waves that are neither exactly in phase or exactly in antiphase?Out of phase.
- 14How can phase and phase difference be measured?By using a phase angle.
- 15What can we use a phasor to show?Where the wave is in its cycle.
- 16How much does the arrow turn as the waves goes through one cycle?2 pi radians/ 360 degrees.
- 17What represents the displacement of the wave at an instant in time?The vertical displacement of the tip of the clock arrow above or below the midpoint (see diagram).
- 18How do you work out this displacement?See diagram.
- 19How can we calculate the displacement when 2 waves superpose?By adding the individual wave displacements together.
- 20What does the length of the phasor arrow represent?The amplitude of the wave.
- 21How can we find the amplitude of the resultant phasor?By adding the phasor arrows together (tip-to-tail)- the arrow sum of the individual components.
- 22What happens when 2 progressive waves of the same frequency are travelling in opposite directions?The waves can appear to stop moving.
- 23What is formed when this happens?A standing/ stationary wave is formed.
- 24What happens when a standing wave forms?The positions of maximum and minimum oscillation do not change.
- 25What are standing waves an example of?Superposition.
- 26When can these waves also be produced?When sound waves and electromagnetic waves superpose.
- 27What 3 things happen when a string is plucked?- Waves move along the string in opposite directions
- Waves reflect at the ends of the string
- Waves superpose as they pass through one another. - 28What are the 3 first standing waves? What does the wavelength = for each?(See diagram)
1) Wavelength = 2L
2) Wavelength = L
3) Wavelength = 2/3L
Where L is the length of the string. - 29What are antinodes?Points of maximum amplitude of oscillation along the string- where the waves meet in phase.
- 30What are nodes?Points of minimum amplitude of oscillation along the string (0)- where the waves meet in antiphase.
- 31How far apart are adjacent nodes?Half a wavelength.
- 32What is the wavelength of the largest standing wave?2 x length of the string.
- 33What is the frequency of vibration of this wave?The lowest frequency of vibration.
- 34What is this frequency called?The fundamental frequency.
- 35Where can standing waves also be formed?In air columns.
- 36How is this used by some instruments?How wind instruments form their notes.
- 37As a sound waves travels along the tube, what happens at the end?The wave reflects.
- 38What do waves travelling up and down the tube do?They superpose with each other.
- 39Which 2 ways can sound be reflected in this tube?-Waves can be reflected from a closed end of a tube
-Waves can be reflected from an open end of a tube. - 40What does this mean?There are 2 distinct sets of standing waves in tubes.
- 41What happens when the waves travelling in opposite directions meet in phase?An antinode is formed.
- 42What happens when the wave meet in antiphase?A node is formed.
- 43What is always present at the open end of a tube?An antinode.
- 44What are 2 standing waves in open tubes and in closed tubes?(See diagram).
- 45Where can you also observe standing waves?In sounds and in microwaves- by placing the source of the waves in front of a wall or reflector.
- 46What do particular separations between the source and reflector give?Standing waves.
- 47When does this happen?When the reflected waves superpose with those from the source.
- 48What is the path difference for a maxima?Path difference = n x wavelength
(Where n is any integer multiple) - 49What is the phase difference for a maxima?0.
- 50What is the path difference for a minima?Path difference = (n+1/2) x wavelength(Where n is any integer multiple)
- 51What is the phase difference for a minima?180 degrees.
- 52So what is the phase difference if the path difference comes out as: - an integer of wavelengths - not an integer of wavelengths.- 0
- Not 0. - 53What is the path difference?The distance between two waves at a specific point.
- 54What is the phase difference?The angle between two phasors at a point.
- 556.2; LIGHT, WAVES, AND REFRACTION.
- 56What happens to waves when they change medium?They change speed- making the light rays bend and change direction.
- 57What is a vacuum?A region of space that contains no matter.
- 58What speed does light travel at in a vacuum?Speed of light.
- 59What is the comparative speed of light in air? Why?Very slightly slower- because the light interacts with electrons in the atoms in the air.
- 60Why is this difference in speed small?Because air is not very dense, so interactions between light and electrons are few.
- 61Why does light travel considerably slower in glass?Because glass is much denser than air, so number of interactions per metre between light and the electrons in the atoms of the glass is much greater.
- 62What is the refractive index?The ratio of the speed of light in one medium to the speed of light in another medium.
- 63What is one equation for the refractive index?n = C1st medium / C2nd medium.
- 64What happens if the 1st medium is a vacuum?The equation gives the refractive index of the material.
- 65What is this known as?The absolute refractive index.
- 66How can refraction be modelled?Using both wave-fronts and light rays.
- 67What would a diagram for light ray refraction look like?(See diagram).
- 68What happens to the ray as it enters glass from air? What is this?It bends towards the normal- an imaginary line at 90 degrees to the air-glass boundary (glass surface).
- 69What is Snell's law?Refractive index of a material = Sini/ Sinr
- 70What can you do with the 2 formulas for the refractive index of a material?Equate them.
- 71What does the refractive index vary with?The wavelength of the light.
- 72What does this explain?Dispersion- why prisms and raindrops disperse light into the colours of the spectrum.
- 73What did Huygens do?Provided an explanation on the behaviour of light, including refraction, using idea that light travelled as a wave.
- 74What did he imagine light as doing?Spreading out as tiny wavelets.
- 75What did he picture every point on a wave-front as?A source of circular wavelets.
- 76What did Huygens suggest about these wavelets?Where they meet in phase they combine to form a new wave-front.
- 77What happens everywhere else?The wavelets from one part of the wave will be in antiphase with those from another part of the wave- so will cancel out.
- 78What must we think of the wavelets from the wave as? What is this an example of?Must think of them as spreading everywhere, but adding up to nothing except where the wave actually travels- example of superposition.
- 79What can we use the model of light as a succession of wave-fronts to do?To explain why light bends as it moves from one material to another (at an angle other than along the normal).
- 80What did Huygens suggest about what happens when a wave-front enters glass from air parallel to the normal?Waves slow down when they enter glass so waves behind 'catch up'
Wavelength is shorter in glass but there is no change in direction.
(See diagram) - 81What did Huygens suggest about what happens when a wave-front enters glass from air at an angle to the normal?Wave-fronts become kinked at the boundary-
Because section of wave-fronts travelling through the air travels faster than the section of the wave-front in the material.
(See diagram) - 82What can we use this model and geometry to do?Explain why ratio of speeds is the same as the ratio of the sini/ sinr.
(See calculations) - 83What can we therefore say?Snell's experimental law matches Huygen's analysis based on light wave-fronts slowing down,
when they travel from air to another transparent material. - 84How can we talk about wavelets in terms of rays?Path of a refracted ray is only path where the wavelets meet in phase, everywhere else cancel out.
- 856.3; PATH DIFFERENCE AND PHASE DIFFERENCE.
- 86Why may designers and architects have to take superposition into account when designing concert halls?Because some rooms have acoustic dead spots- where sound from stage lower volume than expected.
- 87When do acoustic dead spots happen?Sound waves reflected from the walls and ceiling superpose and the amplitude of the wave is reduced.
- 88When is this superposition effect shown every clearly?When 2 loudspeakers emit note of same frequency and amplitude- walking in front of them you will notice positions where sound is louder and quieter.
- 89What would happen if you stand at a region of quiet and turn one of the speakers off?The amplitude of the sound you hear will be increased.
- 90What is interference often used to do?Describe the effect of the superposition of waves.
- 91What does the superposition of waves produce?An interference pattern.
- 92What is an example of this?The alternations of loud and quiet positions in front of the two speakers.
- 93What happens in positions where waves from the 2 speakers meet in phase?A louder sound is heard.
- 94What happens in positions where waves from the 2 speakers meet in antiphase?A quieter sound is heard.
- 95What happens if waves from the 2 speakers are of the same amplitude where they meet in antiphase?They will cancel completely, producing silence.
- 96What is path difference?The difference in path length between the sources and the receiver
(see diagram). - 97What would happen if the path difference were an integer multiple of a wavelength?The waves will meet in phase- increasing the amplitude of the superposed wave form (superposition maximum).
- 98What would happen if the path difference were a half integer multiple of a wavelength?The waves could meet in antiphase- completely cancelling out if the amplitude of each wave is the same (superposition minimum).
- 99What happens when the path difference is 0?The waves will be in phase.
- 100What does this mean?You hear a louder sound when you stand at equal distances from the 2 speakers in the earlier experiment.
- 101What is the path difference when waves meet in phase?n x wavelength
(n is an integer) - 102What is the path difference when waves meet in antiphase?(n+1/2) x wavelength
(n is an integer) - 103What is a stable superposition pattern?One in which the position of the maxima and minima don't change over time.
- 104What is an example of this?If you find a minimum position in front of the loudspeakers and stand there the volume of sound will not change. (unless speakers moved or frequency changed).
- 105When can stable superposition patterns only occur?-When constant phase difference between the waves (waves are coherent).
- 106What is the difference between coherent waves and incoherent wave bursts?Coherent waves have constant phase difference
Incoherent waves bursts have changing phase difference.
(See diagram) - 107When does constructive interference occur? What does this lead to?When waves meet in phase- leading to larger superposition amplitude (maximum).
- 108When does destructive interference occur? What does this lead to?When waves meet in antiphase- leading to lower superposition amplitude (minimum).
- 109What happens in noise-reducing headphones?-Microphone in earpiece detects the background noise that is not stopped by the material of the earpiece.
-Electronic circuitry flips wave-form of this noise so in antiphase with the background noise.
-Flipped noise then fed into headphone speakers- noise and flipped noise cancel out. - 110How would you use superposition to measure the wavelengths of waves?1) Put a transmitter and receiver opposite each other with a mirror above them.
2) Move mirror towards and away from 'line' connecting transmitter and receiver- detecting maxima and minima
3) Measure distances TR and TMR once found maximum.
4) Therefore TMR-TR = n x wavelength
5) Move further away to find next maxima, use this and the previous maxima value n x wavelength to find the wavelength.
(SEE EXPERIMENT) - 1116.4; INTERFERENCE AND DIFFRACTION OF LIGHT.
- 112What can light meeting light in antiphase produce? What is this an example of?A dark band where the 2 waves meet- example of superposition.
- 113What happens when waves pass through a gap of roughly the same width as their wavelength? What is this an example of?The waves spread out- example of diffraction.
- 114What does the amount of the waves spread out depend on?Width of the gap compared to the wavelength of the waves passing through.
- 115What happens as the gap gets smaller for a given wavelength?The greater the spreading out caused by diffraction.
- 116What 3 things does diffraction not alter?The wavelength, speed or frequency of the waves.
- 117What is an example of diffraction?Someone speaking:
person doesn't need to face you for you to hear; sound diffracted from person's mouth and spreads out. - 118Why does the sound diffract around the speaker?Because the wavelength of the sound (around 1m) is so much bigger than the gap the waves are passing through.
- 119Why is it more difficult to observe diffraction in light?Because light does not seem to bend round corners or spread out through slits.
- 120What is the reason for this?Because the wavelength of light is of the order 10^-7 m.
- 121How would diffraction be represented in diagrams?(See diagrams).
- 122What did Young's experiment support?The theory that light travels as waves.
- 123what was Young's experiment?Passed light through 2 pinholes very close together and observed a pattern of dark and bright fringes.
- 124What do modern versions of this experiment use?Slits rather than pinholes.
- 125What is this observed pattern due to?Superposition of light from the 2 slits.
- 126Where are bright fringes and dark patches observed?-Bright fringes; where light from both slits meets at screen in phase.
-Dark patches; where light from both slits meets at screen in antiphase. - 127How could this be shown in diagrams?(See diagrams).
- 128What is this related to?The different path differences at different angles.
- 129Why are the diagrams of the double split experiment only an approximation?Because they show parallel rays of light meeting on a distant screen, where in actual fact parallel lines never meet.
- 130HBecause the distance between the slits and the screen is so large compared to the separation of the slits.
- 131When does the diagram show a situation producing a bright fringe?When the path difference is a whole number of wavelengths
(See diagram). - 132What does the wavelength equal for waves with a path difference of 1 wavelength? What do d and θ represent?Wavelength = dsinθ
d= slit separation
θ= angle made at slits between 1 bright fringe and the next. - 133What would a diagram look like for a path difference of 2 wavelengths?(See diagram)
- 134What can we write for a path difference of n wavelengths?n x wavelength = dsinθn
- 135What does the order of maxima show?The number of wavelengths path difference between light from 2 adjacent slits and the screen.
- 136Therefore, when is the zeroth, first and second order?- n=0 when path difference between 2 adjacent slits and screen is 0.
- n=1 when path difference between 2 adjacent slits and screen is 1 wavelength.
- n=2 when path difference between 2 adjacent slits and screen is 2 wavelengths. - 137What are the angles of orders? What does this mean?Very small- so screen must be good distance away from slits to allow bright and dark fringes to be observed.
- 138What would the diagram showing the geometry of waves meeting at a distant screen look like?(See diagram).
- 139What are the 3 approximations made in this diagram?- Angel θ is very small
- Paths are effectively parallel
- Distance L = slit-screen distance. - 140What is another equation for wavelength obtained from this diagram?Wavelength = (xd/L)
- 141What is a diffraction grating?A multiple slit version of the 2 split-system.
- 142Is the equation (n x wavelength) = dsinθn also usable for gratings?Yes.
- 143What does using a diffraction grating do? Why?Increases brightness of the image on the screen, because more light gets through.
- 144What do they also do?Give a sharper fringe pattern.
- 145What do gratings spread white light into? Why?Into its components colours, because each wavelength of light will produce a maximum at a different angle.
- 146How would you draw a diagram of waves from many sources all being in phase?(See diagram).
- 147What are diffraction gratings often described by?Their number of lines per mm.
- 148How do you calculate the separation of each line (equivalent of slit separation d)?Line separation (m) = 1/ Number of lines per metre.
- 149What can we use phasor thinking to do?Explain diffraction through a narrow aperture (single slit).
- 150What would a diagram of this look like?(See diagram).
- 151What do we imagine as the waves passes through a slit?Each point in the wave-front is a source of new wavelets.
- 152What do we also imagine these as?Rotating phasor arrows.
- 153What do we get when the phasor arrows are all in the same direction?Large resultant, creating a maximum
(See diagram). - 154What happens when the path difference across the whole of the slit is one wavelength at an angle θ?Each phasor reaches screen little out of phase with phasor from the adjacent point
-all phasors add together to get a zero resultant. - 155What is this called?A diffraction minimum.
- 156When does a diffraction minimum occur? What is b?When sinθ = wavelength/b
where b = width of slit. - 157How would you represent this in diagrams?(See diagrams).
- 158So what would the path difference across the whole slit also equal?bsinθ.
- 159What must this situation be?A distant screen with paths nearly parallel and a constant path difference?
- 160What does sinθ <= 1 mean?The highest order maximum will be when sinθ = 1.
- 161What can be shown from this?Number of orders of maxima possible = Slit separation / Wavelength.
- 162Why does the colour change on the tail of a peacock as it moves?Light strikes the feathers and is reflected from tiny ridges on them.
- 163What do these ridges act like?A diffraction grating.
- 164Why will one colour predominate at any angle?Path difference between waves from each ridge
-So at any angle light of that wavelength will be meeting at the eye in phase.
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- AS - Level Physics (AS) Fichas sobre Chapter 6: Wave Behaviour, creado por Matt Clancy el 22/04/2016.
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