6: Wave Behaviour

Question 1

What does the principle of superposition state?

Answer 1

When two or more waves overlap (superimpose), the resultant displacement equals the vector sum of the individual displacements at that position and time

Question 2

Define these words

1. Wavelength
2. Displacement (and amplitude)
3. Frequency
4. Time period

Answer 2

1. Wavelength is the distance between equivalent points on 2 consecutive waves [when distance is plotted against distance] e.g. crest-to-crest
2. Displacement is the distance from the equilibrium position (Amplitude is the maximum displacement from the equilibrium position)
3. Frequency is the number of complete waves passing a given point in one second.[measured in Hz]
4. 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. Note: when displacement is plotted against time, the distance between equivalent points on two consecutive waves is the ‘time period’

Question 3

Interference can be [] or destructive

Answer 3

Constructive

Question 4

What is total destructive interference?

Answer 4

1. When a crest and a trough of equal size (amplitude), combine to give nothing. The two displacements completely cancel each other out.
2. Destructive interference occurs when the two waves are pi radians or lambda/2 or 180^o out of phase.

Question 5

What is an example of constructive interference?

Answer 5

When two crests (or two trougns) from separate waves combine to create a bigger [resultant] crest (or trough).

Constructive interference occurs when the phase difference is 0^o

Question 6

For the interference of the waves to be noticeable, what has to be almost equal?

Answer 6

The amplitudes of the 2 waves

Question 7

1. What is phase?
2. What does a phasor represent?

Answer 7

1. Phase describes the stage of a particular point in a wave cycle
2. The phase of a particular part of the wave

Phasors are rotating arrows that represent the phase of each point on a wave.

Question 8

Which way does a phasor rotate?

Answer 8

Anticlockwise

Question 9

How do you work out rate of phasor rotation?

Answer 9

Phasor rate of rotation is the same as the wave frequency

Question 10

1. What is the phase difference of waves exactly out of phase (antiphase)?
2. What about their phasors?

Answer 10

1. Phase difference is π radians [odd-numbers of π radians].
2. There phasors point in opposite directions

Question 11

What does ‘in phase’ mean for 2 points on a wave?

Answer 11

Two points on a wave are in phase if they are both at the same point in the wave cycle [e.g. crest and crest; trough and trough etc.]

Points that have a phase difference of zero or a multiple of 2π are in phase - their phasors point in the same direction

Question 12

What is the phase difference of two waves emitted from an oscillator?

Answer 12

The waves are in phase so their phase difference is a multiple of 2π

Question 13

To get clear interference patterns the two sources must be []

Answer 13

Coherent

• The waves must have the same frequency and wavelength.
• The wave must also have a constant phase difference between them.

Question 14

What does it mean if two sources are coherent?

Answer 14

1. They have the same wavelength and frequency
2. and
3. Have fixed/constant phase difference between them

Question 15

What affects whether you get constructive or destructive interference at a point?

Answer 15

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)

1. If the phase difference between the waves is a whole number of wavelengths, then constructive interference will take place.
2. If the phase difference between the waves is an odd number of half-wavelengths, then destructive interference will take place

Question 16

What is path difference?

Answer 16

The amount by which the path travelled by one wave from a source is different than the path travelled by the other wave from the source is called the path difference.

Question 17

Describe constructive interference?

Answer 17

1. At any point an equal distance from both sources (that are coherent and in phase), Path difference is zero

or

2.Where the path difference is a whole number of wavelengths

Question 18

What is the path difference for constructive interference?

Answer 18

For constructive interference, the phase difference is nλ where n is an integer

Question 19

What is the path difference for total destructive interference?

Answer 19

Destructive interference occurs when the path differnce is an odd number of half-wavelengths. e.g. (2n+1) λ/2

Question 20

Describe total destructive interference

Answer 20

At any point where the path difference between the waves is an odd number of half wavelengths.

Question 21

define standing waves

Answer 21

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

Question 22

What is a standing wave? (simple)

Answer 22

The superposition of two progressive waves with the same wavelength, moving in opposite directions

Question 23

When do you get a standing wave?

Answer 23

When a progressive wave is reflected at a boundary and superposes with another wave of the same wavelength

Question 24

Is energy transmitted by a standing wave?

Answer 24

No

Question 25

What are resonant frequencies?

Answer 25

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

Question 26

What is a node?

Answer 26

A position, on a standing wave, of zero amplitude

Question 27

What is an anti-node?

Answer 27

A position, on a standing wave, of maximum amplitude

Question 28

Describe the fundamental frequency

Answer 28

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

Question 29

What is another name for the second harmonic?

Answer 29

The first overtone

Question 30

Describe briefly standing waves on stringed instruments

Answer 30

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

Question 31

What does a cathode ray oscilloscopes measure? What does it display?

Answer 31

Voltage It displays waves from an oscillator as a function of voltage over time

Question 32

On a cathode ray oscilloscope, what does the vertical axis show? What does the horizontal axis show?

Answer 32

Vertical: voltage Horizontal: time

Question 33

Describe standing waves and the wind instrument or other air column.

Answer 33

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

Question 34

What is refraction?

Answer 34

The way a wave changes direction as it enters a different medium

Question 35

When does refraction occur?

Answer 35

When the medium a wave is travelling in changes

Question 36

When a wave is refracted does the speed, wavelength, and frequency change?

Answer 36

The speed changes, the frequency stays constant, so the wavelength changes too

Question 37

What happens if light meets a boundary at an angle to the normal? (refraction)

Answer 37

The transmitted ray is bent or refracted as it travels at a different speed in each medium

Question 38

What does the refractive index of a material measure?

Answer 38

How much it slows light down

Question 39

If the ray bends towards the normal – is it speeding up or slowing down? Why? What happens to the wavelength?

Answer 39

Slowing down. The ray is going from a less optically dense material to a more optically dense material. The wavelength decreases

Question 40

What medium does light travel fastest in?

Answer 40

Vacuum

Question 41

Why does light slow down in other materials?

Answer 41

Because it interacts with the particles in them

Question 42

What is the relationship between optical density and speed of light?

Answer 42

The more optically dense a medium is, the more light slows down when it enters it

Question 43

What is the angle of incidence?

Answer 43

The angle the incoming light makes to the normal

Question 44

What is absolute refractive index a measure of?

Answer 44

Optical density

Question 45

Describe refraction

Answer 45

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

Question 46

What is the angle of refraction?

Answer 46

The angle the refracted ray makes with the normal

Question 47

What can you assume that the refractive index of air is?

Answer 47

1 - because the speed of light in air is only a tiny bit smaller than c

Question 48

What is diffraction?

Answer 48

The way that waves spread out as they come through a narrow gap (aperture) or go round obstacles

Question 49

Do all waves diffract?

Answer 49

Yes

Question 50

What does the amount of diffraction depend on?

Answer 50

The wavelength of the wave compared with the size of the gap

Question 51

Describe diffraction when the gap is a lot bigger than the wavelength

Answer 51

Diffraction is unnoticeable

Question 52

Describe diffraction when the gap is several wavelengths wide

Answer 52

Noticeable diffraction

Question 53

When do you get the most diffraction?

Answer 53

When the gap is the same size as the wavelength

Question 54

What can you use to show the diffraction of water waves?

Answer 54

A ripple tank

Question 55

Why can you hear someone through an open door easily, even if they are out of sight?

Answer 55

When sound passes through a doorway, the size of the gap and the wavelength are usually roughly equal, so a lot of diffraction occurs

Question 56

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?

Answer 56

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

Question 57

How can you demonstrate the diffraction of light with a laser light?

Answer 57

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.

Question 58

Laser light is []

Answer 58

Monochromatic

Question 59

How can you demonstrate the diffraction of light using a white light source?

Answer 59

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

Question 60

Describe what happens when a wave meets an obstacle, link to wavelength and diffraction

Answer 60

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

Question 61

What is the diffraction pattern of a light wave passing through an aperture of a similar size to the wavelength?

Answer 61

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.

Question 62

Which fringe is the most intense? What does more intense, in this context (light diffracting though slit), mean?

Answer 62

Central fringe There are more incident photons per unit area in the central fringe than in the other bright fringes

Question 63

The [] the slit, the [] the diffraction pattern

Answer 63

Narrower, wider or wider, narrower

Question 64

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?

Answer 64

Where light passes in a straight line from the slit to the screen All the light waves that arrive there are in phase

Question 65

Describe the phases of the waves that don't arrive at the brightest point, but at other bright points. Phasors? Resultant phasor size?

Answer 65

There is a constant phase difference between the waves arriving there, so the phasors point in slightly different directions and form a smaller resultant

Question 66

Describe the phase difference of the waves at the dark fringes on the screen

Answer 66

The phase difference between the light waves means their phasors add to form a loop, giving a resultant of zero

Question 67

Why is it easy to demonstrate to source interference for either sound of water?

Answer 67

Because they’ve got wavelengths of an easy size that you can measure

Question 68

How do you demonstrate to you source interference with water or sound?

Answer 68

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

Question 69

What are the two ways of demonstrating to source interference for light?

Answer 69

Use to coherent light sources, or use a single laser and shine through two slits (Young’s double slit experiment)

Question 70

Describe the laser light used for Young’s double slit experiment

Answer 70

Laser light is coherent and monochromatic, there’s only one wavelength present

Question 71

Describe the slits for Young’s double slit experiment

Answer 71

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

Question 72

What pattern do you get from the Young’s double slit experiment?

Answer 72

Light and dark fringes, depending on whether constructive or destructive interference is taking place

Question 73

What is the path difference at the first, central, light fringe in Young’s double slit experiment?

Answer 73

Zero

Question 74

What is the path difference of the second light fringe? In Young’s double slit experiment

Answer 74

λ

Question 75

What is the path difference of the first dark fringe? Young’s double slit experiment

Answer 75

λ/2

Question 76

How can you adapt Young’s double slit experiment to observe interference patterns with microwaves?

Answer 76

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

Question 77

What helps to lower the percentage error when calculating the fringe spacing in Young’s double slit experiment?

Answer 77

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

Question 78

What was Young’s experiment evidence for?

Answer 78

The wave nature of light

Question 79

Which phenomena can corpuscular theory explain?

Answer 79

Reflection and refraction, but diffraction and interference are both uniquely wave properties

Question 80

What is corpuscular theory?

Answer 80

Newtons theory suggesting that light was made up of tiny particles, which he called corpuscles

Question 81

What happens when you repeat Young’s double slit experiment but with more than two equally spaced slips?

Answer 81

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

Question 82

What is the advantage of using a diffraction grating with hundreds of slits per millimetre over two slits?

Answer 82

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

Question 83

Diffraction grating is: What is the line of maximum brightness called?

Answer 83

The 0 order line

Question 84

For [] light, all the maxima are sharp lines

Answer 84

Monochromatic (Different for white light)

Question 85

How do you describe the bright lines from diffraction grating patterns?

Answer 85

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

Question 86

Describe at what wavelengths you get the lowest resonant frequency for closed-ended, and open-ended instruments

Answer 86

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

Question 87

Investigation of speed of sound using standing waves: How can you tell when the sound resonates?

Answer 87

This will be when the sound appears loudest

Question 88

When does refraction happen?

Answer 88

When a wave changes speed at a medium boundary

Question 89

Explain refraction

Answer 89

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

Question 90

What does the amount of refraction depend on? What does this imply about focal length?

Answer 90

The wavelength of the light - therefore the focal length for a given lens will change depending on wavelength

Question 91

Describe how density and speed affect/are affected by refraction

Answer 91

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

Question 92

what do phasors have the same frequency as, and how do you determine the length of the phasor

Answer 92

phasors have the same frequency of the wave the amplitude of a wave is the length of the phasor