Combining Waves Flashcards
1
Q
What is superposition?
A
Superposition is when two waves of the same type (e.g. sound waves) overlap and interact. This displacement of the medium where the waves overlap, is the vector. sum of the two wave displacements
2
Q
What is interference?
A
Interference is the name given to the superposition of waves from two coherent sources of waves. interference is constructive if waves are in phase, or destructive if waves are in anti phase (out of phase by 180 degrees)
3
Q
What does it mean if two waves are coherent?
A
Two waves are coherent when they have a fixed phase difference and have the same frequency
4
Q
What is a stationary (or standing) wave?
A
- It is a wave formed by the superposition of two progressive waves of the same frequency and amplitude travelling in opposite directions
- A standing waves consists of nodes and antinodes and is formed by two identical waves travelling in opposite directions
5
Q
What is a node?
A
A node is a point of zero amplitude on a stationary wave
6
Q
What is an antinode?
A
An antinode is a point of maximum amplitude of a stationary wave
7
Q
What is a harmonic?
A
A harmonic is a mode of vibration that is a multiple of the first harmonic
8
Q
What does constructive and destructive interference depend on?
A
- Path difference
1. Whether you get destructive or constructive interference at a point depends on how much further one wave has travelled than the other wave to get to that point
2. 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
3. At any point an equal distance from two sources that are coherent and in phase, you will get constructive interference - You also get constructive interference at any point whether the path different is a whole;e number of wavelengths
- At these points the two waves are in phase and reinforce each other
4. But at point where the path difference is half a wavelength, one and half wavelengths, two and a half wavelengths etc. the waves arrive OUT OF PHASE and you get destructive interference
9
Q
When does constructive interference occur?
A
When the path difference is nlamda, (where n is an integer)
10
Q
When does destructive interference occur?
A
When the path difference is = (2n+1)lamda / 2 = (n+0.5)lamda
11
Q
What are stationary waves and when are they created?
A
- Progressive waves reflected at a boundary can create a stationary wave
1. A stationary (standing) wave is the superposition of two progressive waves, with the same frequency (wavelength), moving in opposite directions
12
Q
What are the properties of stationary waves?
A
- Unlike progressive wave, no energy is transmitted by a stationary wave
- You can demonstrate stationary waves by setting up a driving oscillator at one end of a stretched string with the other end fixed. The wave generated by the oscillator is reflected back and forth
- For most frequencies the resultant pattern is a jumble. However, if 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
- At these ‘resonant frequencies’ you get a stationary wave where the pattern doesn’t move, it just sits there bobbing up and down.
13
Q
What do stationary waves form?
A
- Stationary waves in strings form oscillating ‘loops’ separated by nodes
- Each particle vibrates at right angles to the string
- Nodes are where the amplitude of the vibration is zero
- Antinodes are points of maximum amplitude
- At resonant frequencies, an exact number of half wavelengths fits onto the string
14
Q
What is the first harmonic?
A
- This stationary wave is vibrating at the lowest possible resonant frequency and it has one ‘loop’ with a node at each end
15
Q
What is the second harmonic?
A
- It has twice the frequency of the first harmonic
2. There are two ‘loops’ with a node in the middle and one at each end
16
Q
What is the third harmonic?
A
- The third harmonic is three times the frequency of the first harmonic
- 1.5 wavelengths fits on the string
17
Q
How do you demonstrate two source interference in water and sound?
A
- It is easy to demonstrate two source interference for either sound or water because they have go wavelengths of a handy sizer you can measure
- You need COHERENT sources, which means that the wavelength and frequency have to be the same. The trick is to use the same oscillator to drive both source. For water, one vibrator drives two dippers, for sounds, one oscialltor is connected to two loudspeakers
18
Q
How do you show two source interference for light?
A
- Young’s double slit experiment
1. To see two-source interference with light, you can either use two separate, coherent light sources or you can shine a laser through two slits - Laser light is coherent and monochromatic
2. Young’s doublele slit experiment shines a laser through two slits onto a screen
3. The slits have to be about the same size as the wavelength of the laser light so that it is diffracted - then the light from the slits acts like two coherent point sources
4. You get a pattern of light and dark fringes, depending on whether constructive or destructive interference is taking place. Thomas Young, the first person to do this experiment (with a lamp rather than a lasr), cam up with a equation to work out the wavelength of the light from this experiment
19
Q
How can working with laser be damage and how can you prevent the risks?
A
- Working with laser is very dangerous because laser light is focused into a very direct, powerful beam of monochromatic light
- If you looked at a laser beam directly, your eye’s lens would focus it onto your retina, which would be permanently damaged
- To make sure you don’t cause damage whilst using lasers you should:
1. Never shine the laser towards a person
2. Wear laser safety googles
3. Avoid shining the laser beam at a reflective surface
4. Have a warning sign on display
5. Turn the laser off when it is not needed
20
Q
How can you do a similar experiment with microwaves?
A
- To see interference patterns with microwaves, you can replace the laser and slits with two microwave transmitter cones attached to the same signal generator
- You also need to replace the screen with a microwave receiver probe
- If you move the probe along the path of the green arrow, you’ll get an alternating pattern of strong and weak signal, just like the light and dark fringes on the screen
21
Q
How do you work out the wavelength with Young’s Double Slit Formula?
A
- The fringe spacing (w) (means the distance from the centre of one minimum to the centre of the next minimum or from the centre of one,maximum to the centre of the next maximum), wavelength (lamda), spacing between slits (s) and the distance from the slits to screen (D) are all related by Young’s double-slit formula, which works for all waves
- Since the wavelength of light is so small you can see form the formula that a high ratio of D/s is needed to make the fringe spacing big enough to see
- Rearranging you can use lamda = ws/D to calculate the wavelength of light
- The fringes are so tiny that it is very hard to get an accurate value of w. It is easier to measure across several fringes and then divide by the number of fringe widths between them
22
Q
How is Young’s experiment evidence for the wave nature of EM nature?
A
- Towards the end of the 17th century, two important theories of light were published, one by Issac Newton and other by Huygens. Newton’s theory suggested that light was made up of tiny particles, which he called ‘corpuscles’. And Huygens put forward a theory using waves
- The corpuscular theory could explain reflection and refraction, but diffraction and interference are both uniquely wave properties. If it could be shown that light showed interference patterns, that would help settle the argument once and for all
- Young’;s double-slit experiment (over 100 years later) provided the necessary evidence. It showed that light co;d both diffract (through narrow slits) and interfere (to form the interference pattern on the screen)
23
Q
How do you make interference patterns sharper?
A
- Interference get sharper when you diffract through more slits
1. You can repeat Young’s double-slit experiment with more than two equally spaced slits, you get basically the same shaped pattern as for two slits: BUT the bright bands are BRIGHTER and NARROWER and the dark areas between are DARKER
2. When monochromatic light (one wavelength) is passed through a grating with hundreds of slits per millimetre, the interference pattern is really sharp because there are so many beams reinforcing the pattern
3. Sharper fringes make for more accurate measurements
24
Q
What happens when you use monochromatic light with a diffraction grating?
A
- Monochromatic light on a diffraction grating gives sharp lines
1. For monochromatic light, all the maxima are sharp line (it is different for white light)
2. There is a line of maximum brightness at the centre called the zero order line
3. The lines just ether side of the centeral one are called first order lines. The next pair out are called second order lines and so on
4. For a grating with slits a distance d apart the angle between the incident beam and the nth order maximum is given by dsintheta = nlamda
5. So by observing d, theta, and n you can calculate the wavelength of the light and if the grating has N slits per metre, then the slit spacing, d is just 1/N metres
25
What is fringe spacing equation?
w=lamdaD/s
26
What are the general conclusions from dsintheta = nlamda?
1. If the wavelength is bigger, sintheta is bigger and so theta is bigger. This means that the larger the wavelength the more the pattern will spread out
2. If d is bigger sintheta is amller. This means that the coarser the grating, the less the pattern will spread out
3. Value of sintheta greater than 1 are impossible, so if for a certain n you get a result of more than 1 for sintheta you know that that order does not exist
27
How can diffraction grating be used to identify elements and calculate atomic spacing?
1. White light is really a mixture of colours. If you diffract white light through a grating then the patterns due to different wavelengths within the white light are spread out by different amounts
2. Each order in the pattern becomes a spectrum, with red on the outside and violet on the inside. The zero order maximum stays white because all the wavelengths just pass straight through
3. Astronomers and chemicals often need to study spectra to help identify elements. They sue diffraction gratings rather than prisms because they are more accurate
4. The wavelength of X-rays is of a similar scale to the spacing between atoms in crystalline solids. This means that X-rays will from a diffraction pattern when directed at a thin crystal
5. The crystal acts like a diffraction grating and the spacing between the atoms (slit width) can be found from the diffraction pattern
6. This is called X-ray crystallography and it was used to discover the structure of DNA
28
How do you derive the equation for diffraction grating?
1. At each slit the waves are diffracted. These diffracted waves then interfere with each other to produce an interference pattern
2. Consider the first order maximum. This happens at the angle when the waves from one slit line up with the waves from the next lit that are exactly one wavelength behind
3. Call the angle between the first order maximum and the incoming light theta
4. Now, look at the triangle highlighted in the diagram. The angle theta (using basic geometry), d is the slit pacing and the path difference is lamda
5. So for the first maximum, using trig dsintheta = lamda
6. The other maxima occur when the path difference is 2lamda, 3lamda, 4 lamda etc. SO to make the equation general, just replace lamda with nlamda, where n is an integers, the order of the maximum
29
What is diffraction?
- Waves go round corners and spread out of gaps
- The way that waves spread out as they come through a narrow gap or go round obstacles is called diffraction. All waves diffract, but it's not always easy to observe
- The amount of diffraction depends on the wavelength of the wave compared with the size of the gap
30
How is diffraction affected?
1. When the gap is a lot bigger than the wavelength , diffraction is unnoticeable
2. You get noticeable diffraction through a gap several wavelengths wide
3. You get the most diffraction when the gap is the same size as the wavelength
4. If the gap is smaller than the wavelength, the waves are mostly just reflected back
31
How is sound and diffraction related?
1. When sound passes through a doorway, the size of gap and the wavelength are usually roughly equal, so a lot of diffraction occurs
2. That is why you have no trouble hearing someone through an open door to the next room, even if the other person is out of your line of sight
3. The reason that you can't see him or her is that when light passes through the doorway, it is passing through a gap around a hundred million time bigger that its wavelength - the amount of diffraction is tiny
4. So to get noticeable diffraction with light you must shine it through a very narrow slit.
32
How is a diffraction pattern formed, what type of light is used?
- To observe a clear diffraction pattern for light, you need to use a monochromatic, coherent light source
- Monochromatic just means that all the light has the same wavelength (and frequency) and so is the same colour
- Lasers are monochromatic and coherent light source
33
How can you demonstrate light diffraction patterns with a laser?
1. If the wavelength of light is about the same size as the aperture, you get a diffraction pattern
2. You'll see a central bright fringe (central maximum), with drake and bright fringes alternating on either side
3. The dark and bright fringes are caused by destructive and constructive interference of light waves
34
How does white light diffract?
- Diffracted white light creates a spectra of colour
1. White light is actually a mixture of different colours, each width with different wavelengths
2. When white light is shone through a single narrow slit, all of the different wavelengths are diffracted by different amounts
3. This means that instead of getting clear fringes (As you would with a monochromatic light source) you will get a spectra of colours
35
What does the intensity of the light relate to?
1. The central maximum in a single slit light diffraction pattern is the brightest part of the pattern
2. This is because the intensity of light is highest in the centre
3. Intensity is the power per unit area
4. For monochromatic light, all photons have the same energy, so an increase in the intensity means an increase in the number of photons per second
5. So there are more photons per unit area hitting the central maximum per second than the other bright fringes
36
How does the width of the central maximum vary with wavelength and slit size?
- When light is shone through a single slit, there are two things which affect the width of the central maximum
1. Increasing the slit width decreases the amount of diffraction. The means that central maximum is narrower, and the intensity of the central maximum is higher
2. Increasing the wavelength increases the amount of diffraction. This means the central maximum is wide, and the intensity of the central maximum is lower
37
How can you demonstrate stationary waves with microwaves?
1. Microwaves reflected off a metal plate set up a stationary wave
2. Microwaves stationary wave apparatus (diagram)
3. You can find the nodes and antinodes by moving the probe between the transmitter and reflecting plate
- Microwaves having the transmitter interfere with reflected waves, forming stationary waves
38
How can you demonstrate stationary waves with sound?
1. Powder can show stationary waves in a tube of air
2. Stationary sounds waves are produced in the glass tube
3. The lycopodium powder laid along the bottom of the tube is shaken away from the antinodes but left undisturbed at the nodes (diagram)
39
How can you investigate the factors affecting the resonant frequencies of a string?
1. Start by measuring the mass (M) and length (L) of strings of different types using a mass balance and a ruler. Then fine the mass per unit length of each string (mu) using mu=M/L
2. Set up the apparatus as shown in the diagram (Diagram) with one of your strings. Record mu, measure and record the length (l) and work out the tension (T) using T=mg (where m is the total mass of the masses in kg)
3. Turn on the signal generator and vary the frequency until you find the first harmonic (i.e. a stationary wave that has a node at each end and a single anti node. This is the frequency of the first harmonic,f
- A vibration transducer is connected to a signal generator that tells it the frequency of the wave you want. A vibrating plate on the transducer creates the wave
40
How do you investigate how the length, tension of mass per unit length of the string affects the resonant frequency?
1. Keeping the string type (mu) and the tension (T) in it the same and altering the length (l). Do this by moving the vibration transducer towards or away from the pulley. Find the first harmonic again and record f against l
2. Keeping the string type (mu) and the length (l) the same and adding or removing masses to change the tension (T). Find the first harmonic again and record f against T
3. Keeping the length (l) and tension (T) the same, but using different string samples to vary mu. Find the frist harmonic and record f against mu
- You can do all of this with a different harmonic - just remember to use the same one throughout the experiment so you are comparing the same resonant frequency
41
What should you find in your experiment of investigating the resonant frequencies of a string?
1. The longer the string, the lower the resonant frequency - because the half wavelength at the resonant frequency is longer
2. The heavier (i.e.the more mass per unit length) the sting, the lower the resonant frequency - because waves travel more slowly down the string. For a given length a lower wave speed, c, makes a lower frequency, f
3. The looser the string the lower the resonant frequency - because waves travel more slowly down a loose string
42
What is the frequency of the first harmonic?
The frequency of the first harmonic,f, is: f=1/2lsqrt(t/mu), where l is the string length in m, T is the tension in the string and mu is the mass per unit length of the string
43
What is superposition and when does it happen?
- Superposition happens when two or more waves pass through each other
1. At the instant the waves cross, the displacements due to each wave combine. Then each wave goes on its merry way. You can see this is two pulses are sent simultaneously from each end of the rope
2. The principle of superposition says that when two or more waves cross, the resultant displacement equals the vector sum of the individual displacements
- 'Superposition' means 'one thing on top of another thing'. You can sue the same idea in reverse - a complex wave can be separated out mathematically into several simple sine waves of various sizes
44
What are the two different types of interference?
- Interference can be constructive or destructive
1. A crest plus a crest gives a bigger crest. A trough plus a trough gives a bigger trough . These are both examples of constructive interference
2. A crest plus a trough of equal size gives nothing. The two displacements cancel each other out completely. This is called destructive interference
3. If the crest and the trough are not the same size, then the destructive interference its not total. For the interference to be noticeable, the two amplitudes should be nearly equal
- Graphically, you can superimpose waves by adding the individual displacements at each point along the x-axis, and then plotting them
45
What dopes in phase mean?
-In phase means in step - two points in phase interfere constructively
1. Two points on a wave are in phase if they are both at the same point in the wave cycle. Points in phase have the same displacement and velocity
2 .One complete cycle as an angle of 360 degrees (2pi radians)
3. Two points with a phase difference of zero or a multiple of 360 degrees (i.e.i a full cycle) are in phase
4. Points with a phase difference of odd-number multiples of 180 degrees (pi radians or a half cycle) are exactly out of phase
5. You can also talk about two different waves being in phase. In practice this happens because both waves came from the same oscillator. In other situations there will nearly be a phase difference between two waves from the same oscillator. In other situation there will nearly always be a phase difference between two waves
46
How do you get interference?
- To get interference patterns the two sources must be coherent
1. Interference still happens when you are observing waves of different wavelength and frequency, but it happens in a jumble. In order to get clear interference patterns, the two or more sources must be coherent (and be in phase)
2. Two sources are coherent if they have the same wavelength and frequency and a fixed phase difference between them
- In exam questions, 'the fixed phase difference' is almost certainly going to be zero. The two sources will be in phase
47
How could you check if the microwaves leaving the transmitter were plane polarised?
1. Place a metal grid between the two points and rotate (OR rotate the grid/detector/transmitter and this causes minimum/zero signal)
48
How could you change the speed of waves in a ripple tank?
Change the depth of the water
49
What is amplitude?
MAXIMUM DISPLACEMENT from equilibrium position
