4.4 - Waves Flashcards

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1
Q

What is a wave?

A

The transfer of energy (not matter)

They are formed when a source produces a disturbance eg:
• a continuous vibration
• sudden single movement
• a pulse

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2
Q

What is a progressive wave?

A
  • an oscillation that travels through matter or vacuum

* transfers energy from one place to another, but does not transfer matter

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3
Q

What happens to particles in a medium when a progressive wave passes through?

A
  • they move from their equilibrium position to a new position
  • the particles exert forces on each other
  • a displaced particle experiences a restoring force from its neighbours and is pulled back to its original position
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4
Q

What are transverse waves?

A

Oscillations of particles are perpendicular to the direction of energy transfer

Peaks and troughs are where the oscillating particles are at a maximum displacement from their equilibrium position

Eg:
• waves on surface of water
• EM waves
• S-waves from earthquakes

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5
Q

What are longitudinal waves?

A

Oscillations of particles are parallel to the direction of energy transfer.

Compressions and rarefactions are formed when they travel through a medium

Eg:
• sound waves
• P-waves from earthquakes

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6
Q

What is displacement?

A

Distance any part of a wave has moved from the equilibrium position in a particular direction

A vector, so can have a positive or negative direction

Symbol = s
Unit = metres (m)
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7
Q

What is amplitude?

A

The maximum displacement from equilibrium

Can be positive or negative

Symbol = A
Unit = metres (m)
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8
Q

What is wavelength?

A

Minimum distance between 2 points in phase on adjacent waves

Eg from peak to peak, compression to compression

Symbol = λ
Unit = metres (m)
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9
Q

What is a time period?

A

Aka period of oscillation

The time taken for one oscillation/one wave to move one whole wavelength pasta given point

Symbol = T
Unit = seconds (s)
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10
Q

What is frequency?

A

The number of oscillations per unit time at any point

Symbol = f
Unit = Hz
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11
Q

What is wave speed?

A

Distance travelled by the wave per unit time

Symbol = v (c is light)
Unit = metres per second (ms^-1)
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12
Q

What is phase difference?

A

The fraction of a cycle between waves/oscillations of points on a wave

Measures in degrees/radians

1 wavelength = 360º or 2π radians

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13
Q

What is the wave equation?

A

v = fλ

v = wavespeed 
f = frequency  
λ = wavelength
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14
Q

How is the wave equation derived?

A

v = s/t

From the definition of a period, in 1 second:
t = T
s = 1λ

v = λ/T

T = 1/f

v = fλ

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15
Q

What is the relationship between period and frequency?

A

f = 1/T

Frequency is the inverse of period

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16
Q

What is a wave profile?

A

A graph showing the displacement of the particles in a wave against the distance along the wave

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17
Q

What does it mean if particles are in phase?

A
  • when particles are oscillating perfectly in step with each other
  • eg they both reach their maximum positive displacement at the same time
  • they have a phase difference of a multiple of 2π (0, 2π, 4π etc)
  • can have different amplitudes, but must have the same frequency
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18
Q

What does antiphase mean?

A

Particles oscillating completely out of step with each other (one reaches its maximum positive displacement when the other reaches its maximum negative displacement)

Have a phase difference multiples of π (π, 3π, 5π etc)

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19
Q

What is path difference?

A

The difference in the distance travelled by two waves from the source to a specific point

Measured in metres or fractions of a wavelength

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20
Q

On a wave profile, what value does the distance between 2 peaks represent?

A

Wavelength (λ)

Can also be measured using a trough and a trough, or any point and its corresponding point on another wave

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21
Q

On a displacement-time graph, what value does the maximum displacement represent?

A

Amplitude (A)

Upwards = positive displacement, downwards = negative displacement

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22
Q

On a graph with time on the x-axis and displacement on the y-axis, what value does the distance between 2 peaks represent?

A

The time period (T)

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23
Q

What is reflection?

A

The change in direction of a wave at a boundary between 2 different media, so that the wave remains in the original medium.

Eg light reflecting off a mirrored surface

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24
Q

What is the law of reflection?

A

The angle of incidence is equal to the angle of reflection.

Note: angles are measured from the normal

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25
Q

What effect does reflection have on the wavelength and frequency of a wave?

A

No effect - the stay the same

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26
Q

What is refraction?

A

The change in direction of a wave as it changes speed when it passes from one medium to another (of different density)

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27
Q

How does speed affect how a wave refracts?

A
  • if a wave speeds up, it’ll refract AWAY from the normal

* if a wave slows down, it’ll refract TOWARDS the normal

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28
Q

How do light and sound waves refract?

A

LIGHT
• when entering a denser medium, EM waves slow down and refract towards the normal
• when entering a less dense medium, EM waves speed up and refract away from the normal

SOUND
• when entering a denser medium, sound waves speed up and refract away the normal
• when entering a less dense medium, sound waves slow down and refract towards the normal

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29
Q

What effect does reflection have on the wavelength and frequency of a wave?

A

• frequency remains the same

  • if the wave slows down, wavelength becomes shorter
  • if the wave speeds up, wavelength becomes longer
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30
Q

What is diffraction?

A

The phenomenon in which waves passing through a gap or around an obstacle spread out.

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31
Q

What effect does diffraction have on the properties of a wave?

A

No effect - speed, frequency and wavelength all remain the same

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32
Q

How much does a wave diffract by?

A
  • it depends on the relative sizes of the wavelength and the gap/obstacle
  • diffraction effects become most significant when the size of the gap/obstacle is around the same as the wavelength
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33
Q

What is polarisation?

A

The phenomenon in which a transverse wave only has oscillations in one direction

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34
Q

What does unpolarised mean?

A

When oscillations of a transverse wave occur in many different directions

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35
Q

What does plane polarised mean?

A

When oscillations of a transverse wave are limited to only one plane

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36
Q

What does partially polarised mean?

A

When there are more oscillations of a transverse wave in one particular plane, but the wave is not completely plane polarised

Occurs when transverse waves reflect off a surface

37
Q

What is intensity?

A

Intensity of a progressive wave is the radiant power passing through a surface per unit area

Units watts per square metre (Wm^2)

38
Q

What is the relationship between intensity and distance from a light source?

A

I ∝ 1/r²

I = intensity
r = radius
39
Q

What is the equation for intensity?

A

Intensity = power/area

40
Q

What is the relationship between intensity and amplitude?

A

Intensity ∝ amplitude²

41
Q

What is an electromagnetic wave?

A
  • a transverse wave
  • when electric and magnetic fields oscillate at right angles to each other
  • can travel through a vacuum
42
Q

What are the wavelengths of different types of EM radiation?

A

Gamma rays: <10^-16m to 10^-10m

X-rays: 10^-13m to 10^-8m

UV: 10^-8m to 4x10^-7m

Visible: 4x10^7m to 7x10^-7m

Infrared: 7x10^-7m to 10^-3m

Microwaves: 10^-3m to 10^-1m

Radiowaves: 10^-1m to >10^6 m

43
Q

How can you distinguish between X-rays and gamma rays?

A

X-rays are emitted by fast-moving electrons

Gamma rays are emitted from unstable nuclei

44
Q

What are the properties of electromagnetic waves?

A
They can be:
   • reflected
   • refracted
   • diffracted
   • plane polarised

They can travel through a vacuum

All EM travel through a vacuum at 3x10^8 metres per second, which is approximately the speed of EM waves in air

45
Q

How can unpolarised EM waves be polarised?

A
  • polarising filters for light

* metal grilles for microwaves?

46
Q

What are polarisers?

A

Filters that polarise EM waves

The nature of the polariser depends on the part of the EM spectrum to be polarised

All polarisers only let waves with a particulate orientation through

47
Q

What are polarising filters?

A
  • polarises light
  • they are plastic films that contain very long crystals, which polarise light
  • they are used in sunglasses and over liquid crystal displays eg watches
48
Q

What happens when you place 2 polarising filters together and rotate them?

A
  • unpolarised light passing through the first filter is plane polarised
  • if the second polarising filters (sometimes called analyser) is in the same plane as the first, the plane polarised light passing through is unaffected.
  • if the second Polaroid is slowly rotated, the intensity of light transmitted drops.
  • when the second filter has turned 90º, no light is transmitted,titled and the intensity falls to 0.
49
Q

Howe do metal grilles polarise microwaves?

A

same way as polarising filters - they only allow microwaves through which oscillate in a particular plane

50
Q

How can microwaves and metal grilles be used to demonstrate polarisation?

A

Place a metal grille between a source of plane polarised microwaves and a receiver

Rotate the metal grille through 180º, around the axis of the beam

Note the intensity of microwaves recorded by the receiver

51
Q

What is the refractive index?

A
  • a property of a material
  • tells you how much a material refracts light
  • the greater the refractive index, the more light is refracted towards the normal when it enters.

Calculated by n=c/v

n = refractive index
c = speed of light in a vacuum
v = speed of light through the material
52
Q

What is the refraction law?

A

at a boundary:

n sinθ = k

n = refractive index of the material
θ = angle between the normal and the incident ray
k = a constant
53
Q

What is Snell’s Law?

A

Describes what happens when light travels from one medium to another

n1 sinθ1 = n2 sinθ2

n1 = refractive index of original medium
sinθ1 = angle of ray in original medium
n2 = refractive index of second medium
sinθ2 = angle of ray in second medium
54
Q

What is total internal reflection?

A

The reflection of all light hitting a boundary between 2 media back into the original medium

Conditions:
• the light must originally be travelling through a medium with a higher refractive index than the other medium at the boundary

• the incidence angle at the boundary must be greater than the critical angle

55
Q

What is the critical angle?

A

The angle of incidence at the boundary between 2 media that will produce an angle of refraction of 90º

56
Q

How can you derive the equation for the critical angle when light moves through a medium into air?

A

At the critical angle C, θ(air)= 90º
Using Snell’s law:
n1sinC= n(air)sin90º

sin90 and n(air) = 1
nsinC = 1

sinC = 1/n

57
Q

What is superposition?

A

Overlap of 2 waves at a point in space

58
Q

What is the principle of superposition of waves?

A

When 2 waves meet at a point, the resultant displacement at that point is equal to the sum of displacements of the individual waves

59
Q

What is interference?

A

Superposition of 2 progressive waves from coherent sources to produce a resultant wave with a displacement equal to the sum of the individual displacements from the 2 waves

60
Q

What is constructive interference?

A

Superposition of 2 waves in phase so that the resultant wave has a greater amplitude than the original waves

Since intensity ∝ amplitude², the increased amplitude results in increased intensity

61
Q

What is destructive interference?

A
  • Superposition of 2 waves in antiphase so that the waves cancel each other out and the resultant wave has a smaller amplitude than the original waves
  • If the 2 waves have the same amplitude, the resultant wave will have 0 amplitude and therefore 0 intensity
62
Q

What is an interference pattern?

A

A pattern of constructive and destructive interference formed as waves overlap

63
Q

What is coherence?

A

When waves emitted from 2 wave sources have a constant phase difference

This means the waves must also have the same frequency

64
Q

What is path difference?

A

The difference on the distance travelled by 2 waves from the source to a specific point

Measured in wavelengths (λ) or metres (m)

65
Q

What are maxima?

A

Points of greatest amplitude in an interference pattern, produced by constructive interference

Occurs when:
• waves meet in phase
• path difference is a multiple of λ

66
Q

What are minima?

A

Points of the least amplitude in an interference pattern, produced by destructive interference

Occurs when:
• waves meet in antiphase
• path difference is an odd number of half wavelengths, (n+1/2)λ

67
Q

Interference with sound

A
  • 2 loudspeakers connected to the same signal generator will emit coherent sound waves
  • the interference pattern consists of a series of maxima (loud areas) and minima (quiet areas)
  • maxima and minima can be detected by ear or by microphone
68
Q

Interference with microwaves

A
  • producing coherent sources of microwaves can be difficult, so a single source is used with a double slit
  • the microwaves diffract, and then overlap to form an interference pattern which can be detected with a microwave receiver connected to an oscilloscope or voltmeter
69
Q

Describe Young’s Double slit experiment

A
  • he used a monochromatic source of light (which can be achieved by using a colour filter which only allows a specific frequency of light through)
  • the light passes through a narrow single slit to diffract the light.
  • light diffracting from the single slit reaches the double slit in phase. It then diffracts again from the double slit
  • each slit acts as a source of coherent waves, which spread from each slit, overlapping and forming an interference pattern due to constructive and destructive interference
  • the interference pattern can be seen on a screen as alternating bright and dark fringes
70
Q

What does Young’s double-slit experiment prove?

A

That light is a wave

71
Q

How can you work out the wavelength of a wave producing an interference pattern from 2 coherent sources?

A

λ = ax/D

λ = wavelength 
a = distance between slits/ coherent sources 
x = distance between 2 maxima 
D = distance from source to screen

NOTE: this equation only works when a &laquo_space;D

72
Q

What is a stationary wave?

A
  • aka standing wave
  • a wave that remains in a constant position with no net transfer of energy
  • characterised by nodes and antinodes
73
Q

How do stationary waves form?

A
  • a progressive wave is produced and reflected
  • the reflected wave interferes with the incident wave
  • this produces a resultant wave with nodes where there is destructive interference and antinodes where there is constructive interference
74
Q

What are the conditions for the production of stationary waves?

A
  • the wave generator must produce a whole number of waves in the time it takes for the wave to get to the end and back again
  • the waves must have the same wavelength and frequency
75
Q

What is a node?

A

A point on the stationary wave where amplitude is always 0

76
Q

What is an antinode?

A

A point on a stationary wave with the maximum displacement

77
Q

What is the separation between 2 nodes?

A

Half the wavelength of the original progressive wave (λ/2)

78
Q

How does phase difference change across a stationary wave?

A

In between adjacent nodes, all particles oscillate in phase with each other - they reach their maximum positive displacement at the same time

On different sides of a node, particles are in antiphase - particles on one side of the node reach their positive maximum displacement as particles on the opposite side reach their maximum negative displacement

79
Q

Compare stationary (S) and progressive (P) waves

A

ENERGY TRANSFER
P - energy transferred in direction of wave
S - no net energy transfer

WAVELENGTH
P - minimum distance between 2 adjacent points oscillating in phase (eg peak and peak)
S - twice the distance between adjacent nodes/antinodes

FREQUENCY:
P - all particles oscillate at the same frequency
S - all particles other than nodes vibrate at the same frequency

AMPLITUDE
P - amplitude is constant
S - amplitude varies (max at antinode, 0 at node)

PHASE DIFFERENCE
P - (2π/λ)x, where x is distance between particles
S - nπ, where n is the number of nodes between 2 particles

80
Q

How can you form a stationary wave using microwaves?

A
  • reflect microwaves off a metal sheet so that the 2 microwaves of the same frequency travel in opposite directions
  • reflected microwaves superimpose with incident waves
  • this produces nodes and antinodes
81
Q

How are stationary waves produced on a string?

A
  • the string is fixed at both ends
  • a progressive wave is produced along the string (either by plucking or a vibration generator)
  • the progressive wave is reflected at the fixed end
  • reflected wave interferes with the incident wave
  • where there is destructive interference, nodes are produced
  • where there is constructive interference, antinodes are produces
82
Q

What is the fundamental mode of vibration?

A

A vibration at the fundamental frequency producing a standing wave with one antinode

83
Q

What is the fundamental frequency?

A
  • aka first harmonic, f0

* the frequency required to produce a standing wave with a single antinode in the centre and 2 nodes at either end

84
Q

What is a harmonic?

A

A whole number multiple of the fundamental frequency

85
Q

How do you work out wavelength of a stationary wave on a string?

A

λ = 2L/n

λ = wavelength, metres
L = length of string, metres
n =  mode of vibration (how many antinodes there are)
86
Q

How are stationary waves formed in tubes that are closed at one end and open at the other?

A

There must be a node at the closed end and an antinode at the open end

This means that there can only be odd harmonics

87
Q

How do you work out the wavelength of a standing wave in an open-closed tube?

A

λ = 4L/n

λ = wavelength
L= length of tube
n = mode of vibration
88
Q

How do stationary waves form in an open-open tube?

A
  • both ends must have an antinode

* harmonics are possible at all integer multiples of the fundamental frequency

89
Q

How do you work out the wavelength of a standing wave in an open-closed tube?

A

λ = 2L/n

λ = wavelength, metres
L = length of tube, metres
n =  mode of vibration