6: Wave Behaviour Flashcards
What does the principle of superposition state?
When two or more waves overlap (superimpose), the resultant displacement equals the vector sum of the individual displacements at that position and time
Define these words
- wavelength
- displacement (and amplitude)
- frequency
- time period
Wavelength is the distance between equivalent points on 2 consecutive waves e.g. crest to crest or trough to trough
Displacement is the distance from the equilibrium position (amplitude is the maximum displacement from the equilibrium position)
Frequency is the number of complete waves passing a given point in one second.
Time period is the time taken for a wave to completely pass through any given point. This is the reciprocal of the frequency: 1/time period = frequency & 1/frequency = time period
Interference can be [] or destructive
Constructive
What is total destructive interference?
When a crest and a trough of equal size (amplitude), combine to give zero amplitude
What is an example of constructive interference?
When two crests combine to create a bigger crest (a crest with a larger amplitude)
What is phase?
What does a phasor represent?
Phase describes the stage in a wave cycle
The phase of each point on the wave
Which way does a phasor rotate?
Anticlockwise
How do you work out the rate of phasor rotation
Phasor rate of rotation is the same as wave frequency
What is the phase difference of waves exactly out of phase (antiphase)?
What about their phasors?
The phase difference is an odd-numbers of π radians.
Their phasors point in opposite directions
What does ‘in phase’ mean for 2 points on a wave?
Two points on a wave are in phase if they are both at the same point in the wave cycle
Points that have a phase difference of zero or a multiple of 2π are in phase - their phasors point in the same direction
What is the phase difference of two waves emitted from an oscillator?
They are in phase so their phase difference is a multiple of 2π
To get clear interference patterns the two sources must be []
coherent
What does it mean if two sources are coherent?
They have the same wavelength and frequency and a fixed phase difference between them
What affects whether you get constructive or destructive interference at a point?
Phase difference - depends on how much further one wave has travelled than the other wave to get to that point (assuming the sources are coherent and in phase)
What is path difference?
The amount by which the path travelled by one wave is longer than the path travelled by the other wave is called the path difference
Describe constructive interference
At any point an equal distance from both sources (that are coherent and in phase), or where the path difference is a whole number of wavelengths
What is the path difference for constructive interference?
nλ where n is an integer
What is the path difference for total destructive interference?
(2n+1) λ/2
n is an integer.
i.e. a whole number of half wavelengths
Describe total destructive interference
At any point where the path difference is an odd number of half wavelengths
Define standing waves
transmitted wave reflected at boundary with a 180 degrees phase change. transmitted and reflected waves superpose creating nodes and antinodes. at certain frequencies positions of nodes and antinodes are constant, resulting in a standing wave
What is a standing wave? (simple)
The superposition of two progressive waves with the same wavelength, moving in opposite directions
When do you get a standing wave?
When a progressive wave is reflected at a boundary and superposes with another wave of the same wavelength
Is energy transmitted by a standing wave?
No
What are resonant frequencies?
Frequencies where the oscillator happens to produce an exact number of waves in the time it takes for a wave to get to the end and back again, then the original and reflected waves reinforce each other
What is a node?
A position, on a standing wave, of zero amplitude
What is an anti-node?
A position, on a standing wave, of maximum amplitude
Describe the fundamental frequency
The standing wave is vibrating at the lowest possible frequency, the fundamental frequency This is the first harmonic. It has one loop with the node at each end
What is another name for the second harmonic?
The first overtone
Describe briefly standing waves on stringed instruments
They are transverse standing waves. Your finger or the bow sets the string vibrating at the point of contact. Waves are sent out in both directions and reflected back at both ends
What does a cathode ray oscilloscopes measure? What does it display?
Voltage It displays waves from an oscillator as a function of voltage over time
On a cathode ray oscilloscope, what does the vertical axis show? What does the horizontal axis show?
Vertical: voltage Horizontal: time
Describe standing waves and the wind instrument or other air column.
They are longitudinal standing waves If a source of sound is placed at the open end of a wind instrument, there will be some frequencies for which resonance occurs and a standing wave is set up Nodes form at close ends. Antinodes form at the open ends
What is refraction?
The way a wave changes direction as it enters a different medium
When does refraction occur?
When the medium a wave is travelling in changes
When a wave is refracted does the speed, wavelength, and frequency change?
The speed changes, the frequency stays constant, so the wavelength changes too
What happens if light meets a boundary at an angle to the normal? (refraction)
The transmitted ray is bent or refracted as it travels at a different speed in each medium
What does the refractive index of a material measure?
How much it slows light down
If the ray bends towards the normal – is it speeding up or slowing down? Why? What happens to the wavelength?
Slowing down. The ray is going from a less optically dense material to a more optically dense material. The wavelength decreases
What medium does light travel fastest in?
Vacuum
Why does light slow down in other materials?
Because it interacts with the particles in them
What is the relationship between optical density and speed of light?
The more optically dense a medium is, the more light slows down when it enters it
What is the angle of incidence?
The angle the incoming light makes to the normal
What is absolute refractive index a measure of?
Optical density
Describe refraction
When a ray of light meets a boundary between one medium and another, some of its energy is reflected back into the first medium and the rest of it is transmitted through into the second medium
What is the angle of refraction?
The angle the refracted ray makes with the normal
What can you assume that the refractive index of air is?
1 - because the speed of light in air is only a tiny bit smaller than c
What is diffraction?
The way that waves spread out as they come through a narrow gap (aperture) or go round obstacles
Do all waves diffract?
Yes
What does the amount of diffraction depend on?
The wavelength of the wave compared with the size of the gap
Describe diffraction when the gap is a lot bigger than the wavelength
Diffraction is unnoticeable
Describe diffraction when the gap is several wavelengths wide
Noticeable diffraction
When do you get the most diffraction?
When the gap is the same size as the wavelength
What can you use to show the diffraction of water waves?
A ripple tank
Why can you hear someone through an open door easily, even if they are out of sight?
When sound passes through a doorway, the size of the gap and the wavelength are usually roughly equal, so a lot of diffraction occurs
Why can you not always see a person the other side of an open doorway (slightly out of sight) even though you can hear them?
When light passes through the doorway, it is passing through a gap around a hundred million times bigger than its wavelength - the amount of diffraction is tiny
How can you demonstrate the diffraction of light with a laser light?
Shine the laser light though a very narrow slit onto a screen. You can alter the amount of diffraction by changing the width of the slit.
Laser light is []
Monochromatic
How can you demonstrate the diffraction of light using a white light source?
You need a set of colour filters. The size of the slit can be kept constant while the wavelength is varies by putting different colour filters over the slit
Describe what happens when a wave meets an obstacle, link to wavelength and diffraction
You get diffraction around the edges. Behind the obstacle is a ‘shadow’, where the wave is blocked. The wider the obstacle compared with the wavelength of the wave the less diffraction you get, and the longer the shadow
What is the diffraction pattern of a light wave passing through an aperture of a similar size to the wavelength?
You get a diffraction pattern of dark and light fringes. The pattern has a bright central fringe with alternating dark and bright fringes on either side of it.
Which fringe is the most intense? What does more intense, in this context (light diffracting though slit), mean?
Central fringe There are more incident photons per unit area in the central fringe than in the other bright fringes
The [] the slit, the [] the diffraction pattern
Narrower, wider or wider, narrower
Describe the phase of the waves at the brightest point of a diffraction pattern. Where has the wave travelled to get to the brightest point?
Where light passes in a straight line from the slit to the screen All the light waves that arrive there are in phase
Describe the phases of the waves that don’t arrive at the brightest point, but at other bright points. Phasors? Resultant phasor size?
There is a constant phase difference between the waves arriving there, so the phasors point in slightly different directions and form a smaller resultant
Describe the phase difference of the waves at the dark fringes on the screen
The phase difference between the light waves means their phasors add to form a loop, giving a resultant of zero
Why is it easy to demonstrate to source interference for either sound of water?
Because they’ve got wavelengths of an easy size that you can measure
How do you demonstrate to you source interference with water or sound?
You need coherent sources (wavelength and frequency the same), eg. use the same oscillator to drive both sources. For water, one vibrator drives to dippers. For sound, one oscillators connected to loudspeakers
What are the two ways of demonstrating to source interference for light?
Use to coherent light sources, or use a single laser and shine through two slits (Young’s double slit experiment)
Describe the laser light used for Young’s double slit experiment
Laser light is coherent and monochromatic, there’s only one wavelength present
Describe the slits for Young’s double slit experiment
They have to be about the same size as the wavelength of the laser light to say that it is defective – then the light from the slits acts like 2 coherent point sources
What pattern do you get from the Young’s double slit experiment?
Light and dark fringes, depending on whether constructive or destructive interference is taking place
What is the path difference at the first, central, light fringe in Young’s double slit experiment?
Zero
What is the path difference of the second light fringe? In Young’s double slit experiment
λ
What is the path difference of the first dark fringe? Young’s double slit experiment
λ/2
How can you adapt Young’s double slit experiment to observe interference patterns with microwaves?
You can replace the laser and slits with two microwave transmitter cones attached to the same signal generator You need to replace the screen with a microwave receiver probe If you move the probe perpendicular to the direction of the waves, you’ll get an alternating pattern of strong and weak signals – just like the light and dark fringes on the screen
What helps to lower the percentage error when calculating the fringe spacing in Young’s double slit experiment?
The fringes are so tiny that it’s very hard to get an accurate value of X. It’s easier to measure across several fringes then divide by the number of fringe widths between them
What was Young’s experiment evidence for?
The wave nature of light
Which phenomena can corpuscular theory explain?
Reflection and refraction, but diffraction and interference are both uniquely wave properties
What is corpuscular theory?
Newtons theory suggesting that light was made up of tiny particles, which he called corpuscles
What happens when you repeat Young’s double slit experiment but with more than two equally spaced slips?
You get the same shaped pattern as the two slits – but the bright bands are brighter and narrower, and the dark areas between are darker
What is the advantage of using a diffraction grating with hundreds of slits per millimetre over two slits?
When monochromatic light is passed through a grating with loads of slits, the interference pattern is really sharp because there are so many beams reinforcing the pattern. Sharper fringes make for more accurate measurements
Diffraction grating is: What is the line of maximum brightness called?
The 0 order line
For [] light, all the maxima are sharp lines
Monochromatic (Different for white light)
How do you describe the bright lines from diffraction grating patterns?
The lines either side of the central one are called first order lines. The next pair out are called 2nd order lines and so on
Describe at what wavelengths you get the lowest resonant frequency for closed-ended, and open-ended instruments
You get the lowest resonant frequency when the length of the pipe is a quarter wavelength If both ends are open, you get the lowest resonant frequency when the length of the pipe is a half wavelength
Investigation of speed of sound using standing waves: How can you tell when the sound resonates?
This will be when the sound appears loudest
When does refraction happen?
When a wave changes speed at a medium boundary
Explain refraction
When a ray of light meets a boundary between one medium and another, some of its energy is reflected back into the 1st medium and the rest of it is transmitted through into the 2nd medium
What does the amount of refraction depend on? What does this imply about focal length?
The wavelength of the light - therefore the focal length for a given lens will change depending on wavelength
Describe how density and speed affect/are affected by refraction
If light meets the boundary at an angle to the normal, the transmitted ray is bent/refracted as it travels at a different speed in each medium The more optically dense a material is, the more slowly light travels in it
what do phasors have the same frequency as, and how do you determine the length of the phasor
phasors have the same frequency of the wave
the amplitude of a wave is the length of the phasor
