module 4 electrons, waves & photons - wordpress.com · 2019. 5. 9. · stationary waves...
TRANSCRIPT
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Module 4 Electrons, Waves & Photons
Unit 4 Waves
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You are here!
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4.4 Waves
• 4.4.1 Wave Motion
• 4.4.2 Electromagnetic Waves
• 4.4.3 Superposition
• 4.4.4 Stationary Waves
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4.4.1 Wave Motion
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What are some of the words used to describe waves?
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Progressive Waves
• An oscillation that can travel from one place to another.– Some need matter to travel through (sound).
– Some can travel through a vacuum (light).
• Progressive waves transfer energy but not matter.– Matter particles oscillate about a fixed point.
• As the oscillating matter particles are pulled from their original equilibrium position, they experience a restoring force which pushes them back again.
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Two types of Progressive Waves
• Transverse waves– Oscillations are perpendicular to the direction of
energy transfer.– Waves have peaks & troughs.– Eg. Electromagnetic waves, ripples on water, S-waves
from earthquakes.
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Transverse Waves
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Two types of Progressive Waves
• Longitudinal waves– Oscillations are parallel to the direction of energy
transfer.
– Waves have compressions & rarefactions.
– Eg. Sound, P-waves from earthquakes.
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Longitudinal Waves
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Wave Equations - Terminology
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The Wave Equations
𝑣 = 𝑓𝜆 Where:
v = Velocity (wave speed), ms-1
f = Frequency (No of waves per second), Hz𝜆 = Wavelength, m
T = Period of Oscillation, s
𝑓 =1
𝑇
𝑣 =𝜆
𝑇So:
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How can we represent waves
visually?
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Displacement – Distance Graphs
• Used to measure Amplitude and wavelength for both types of wave.• Think about displacement of a slinky at different distances from your
hand.
Distance from start / m
Displacement from equilibrium/ m
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Phase Difference
• The difference between the displacements of two particles on a wave (or on different waves).
• Often measured in degrees (or radians).
• 360o (2𝜋 radians)represents one complete cycle.
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Ph
ase
Dif
fere
nce
s
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Displacement – Time Graphs
• Used to measure Amplitude and Period for both types of wave.
Displacement from equilibrium/ m
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Longitudinal waves can also be represented this way.
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What’s the difference between
reflection, refraction & diffraction?
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Reflection
• When a wave changes direction at a boundary between two different media, with the wave remaining in the original medium.
Ray Diagram Wave Diagram
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Reflection of circular waves
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Refraction• When a wave changes direction as it changes speed
when it passes from one medium to another.
Refraction affects the wavelength but not frequency, so the wave speed is changed.
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Diffraction
• Waves spread out as they pass through a gap or travel around an obstacle.– Speed, wavelength and frequency of the wave all stay constant during
diffraction.
• The degree of diffraction depends on the relative size of the gap and the wavelength.– Diffraction is much greater when the gap is the same size as the
wavelength.
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Diffraction around obstacles
• The longer the wavelength the greater the diffraction.
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Polarisation
• As transverse waves travel their oscillations occur at a variety of directions.
• Polarised waves all oscillate in the same direction.– This confines the waves to a single plane.
– The plane contains the direction of oscillations and the direction of energy transfer.
– We say the waves have been plane polarised.
• Longitudinal waves have oscillations which are already limited to one plane so cannot be polarised.
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Spot the spelling mistake
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Why does the intensity of light
reduce with distance travelled?
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Intensity
• The radiant power passing through a surface per unit area.
• Units of intensity: Watts per square metre (Wm-2)
𝐼 =𝑃
𝐴
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Intensity v Distance
• When a wave radiates out from a source in all directions its intensity will vary with the distance travelled.
• How?
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Intensity v Distance
• For a point source of light, energy radiates in all directions.
• The intensity of light at different distances is proportional to 1/r2 where r is the distance from source to observer.
This relationship is called the inverse square law.
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Intensity v Distance
• Doubling the distance reduces the intensity by a factor of 4 (22).
• The total radiant power of the source is spread over the surface of a sphere.
𝐼 =𝑃
𝐴=
𝑃
4𝜋𝑟2
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Intensity v Amplitude
• Intensity of water waves also drops as they radiate outwards.
• The height (amplitude) of the ripple decreases with distance travelled.
• Amplitude is proportional to speed of the oscillating particles. Particle speed is related to Energy by:
𝐸𝐾 = ൗ1 2 𝑚𝑣2
• So for any wave, the intensity is proportional to the square of its amplitude:
𝑰𝒏𝒕𝒆𝒏𝒔𝒊𝒕𝒚 ∝ (𝒂𝒎𝒑𝒍𝒊𝒕𝒖𝒅𝒆)𝟐
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4.4.1 Wave Motion (review)
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4.4.2 Electromagnetic
Waves
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What are electromagnetic
waves
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Electromagnetic waves• Transverse waves.• Can travel through a vacuum.• No particles to oscillate
• EM waves can be imagined as oscillating electric & magnetic fields at right angles to each other.
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EM Spectrum
• As the song goes, EM waves are classified according to their wavelengths.
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Properties of EM Waves
• Can be
– Reflected
– Refracted
– Diffracted
– Plane polarised
• All EM waves travel at the same speed in a vacuum (the speed of light, c, 3.00x108ms-1)
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What is the wavelength of radio 1 broadcasts?
• Frequency: 99.1 MHz
𝑣 = 𝑓𝜆
𝑐 = 𝑓𝜆
𝜆 =𝑐
𝑓=3.00 × 108
9.91 × 107= 3.03𝑚
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Polarisation of EM Waves
• Naturally occurring EM waves are unpolarised.– The EM fields oscillate in random directions.
• Filters can be used to polarise the waves.
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A second filter can prevent all waves
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Refractive Index
• Light is refracted by different amounts by different materials at a boundary.
• The angle of refraction depends on the change in wave speed as the light crosses a boundary.
• Each material has a property called a refractive index.
𝑛 =𝑐
𝑣
Where: n = refractive index of a materialc = speed of light in a vacuumv = speed of light through the material
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What is the speed of light through glass?
𝑛 =𝑐
𝑣
𝑣 =𝑐
𝑛
𝑣 =𝑐
𝑛=3.00 × 108
1.52= 1.97 × 108
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Refraction Law
• For a specific boundary, the ratio between the two refractive indices equals the ratio between the sines of the refractive angles.
𝑛1𝑛2
=sin 𝜃2sin 𝜃1
𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
𝑛 sin 𝜃 = Constant, k
So,
And,
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Total Internal Reflection
• Occurs when light strikes a boundary with a large enough angle to the normal:
– Light must be travelling through the medium with the higher refractive index.• Eg, from water to air not the other way round.
– The angle at which light hits the boundary must be above a critical angle.• This angle depends on the refractive indices of the
media.
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Total Internal Reflection
𝑛𝑤 sin 𝜃𝑤 = 𝑛𝑎 sin 𝜃𝑎 Using this equation, we can calculate the critical angle (C) from the refractive indices:
𝑛𝑤𝑠𝑖𝑛𝐶 = 𝑛𝑎𝑠𝑖𝑛90
𝑛𝑤𝑠𝑖𝑛𝐶 = 1 𝑥 1𝑠𝑖𝑛𝐶 =
1
𝑛𝑤
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Determining Refractive Index from Critical Angle
• Practical
𝑛𝑔𝑠𝑖𝑛𝐶 = 𝑛𝑎𝑠𝑖𝑛90 𝑛𝑔 =1
𝑠𝑖𝑛𝐶
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4.4.2 Electromagnetic
Waves (review)
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4.4.3 Superposition
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What happens when waves
collide?
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Superposition
• When 2 waves of the same type meet, they can pass through each other.
• Where they overlap they superpose, with the resultant displacement equal to the sum of the displacement of the individual waves.
• Remember that displacement is a vector quantity so the superposed wave may have a higher or lower resultant displacement than the original.
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Interference
• Similar to superposition.
• A superposition of progressive waves.
• Here the waves are continuous rather than single pulses.
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Constructive interference
Destructive interference
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How does interference affect intensity?
• Since, intensity = (amplitude)2
– Constructive interference will increase the amplitude and so increase the intensity of the wave.
• Light will become brighter
• Sound will become louder
– Destructive waves have the opposite effect.
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Are all interference patterns the
same?
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Nope!• Look at the interference pattern between these waves.
• These superposed waves are either interfering constructively or destructively but the pattern is changing.
• Because the waves have different frequencies and varying phase differences.
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What happens when two sources have the same frequency and a constant
phase difference?
• Here the two waves show a stable interference pattern.
• These waves are said to be coherent – they have the same frequency and so have a constant phase difference.
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Path Difference
• Waves emitted from two different but coherent sources interfere with a series of maxima and minima.– At the maxima they interfere constructively.
– At the minima they interfere destructively.
• Maxima and minima are caused because even though the two waves start off in phase, they travel different distances to reach a certain point and may end up either in phase or in antiphase.
• These different distances are called path differences.
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Show the maxima and minima
Crest
Trough
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Maxima Minima
m = path difference in wavelengths
Central Maxima1st order
Maxima
2nd order Maxima
2nd order Minima
1st order Minima
0 Phase𝜋 Phase
2𝜋 Phase3𝜋 Phase
4𝜋 Phase
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Interference of sound
• Set sig gen to 1kHz
• Set speakers 0.5m apart
• Plot interference pattern using masking tape on table.
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Newton thought light was made of particles. Young
showed light to be a wave…
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Young’s Double Slit Experiment
Light / dark maxima & minima are called fringes.
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Calculating wavelength of light
a = separation between the two slitsD = Distance between slits and a distant screen, D>>a.x = Distance between fringe central maxima and 1st order maxima.
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Calculating wavelength of light
Since:D is much greater than a.
So:The two shaded triangles are practically congruent.𝜃1 𝑎𝑛𝑑 𝜃2 are practically the same and are very small.The path difference (S1 to P) is therefore equal to 1 whole wavelength.
sin 𝜃1 =𝜆
𝑎= tan𝜃2 =
𝑥
𝐷
𝜆
𝑎=𝑥
𝐷𝜆 =
𝑎𝑥
𝐷So So
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Limitations of
• The equation only applies when D is much greater than a.
𝜆 =𝑎𝑥
𝐷
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4.4.3 Superposition(review)
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4.4.4 Stationary Waves
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What is a stationary
wave?
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Stationary waves
• Stationary waves (or standing waves) are not single waves at all.
• They are superposed progressive waves which have the same frequency travelling in opposite directions
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Forming stationary waves
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• The simplest stationary wave pattern as shown here, consists of a point of no displacement at both ends, called nodes and a point of maximum amplitude midway between the adjacent nodes, called anti nodes.
• This is called the first harmonic on a string.
• Distance between adjacent nodes= ½λ
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• If the frequency of the waves along the ropes from either end is raised steadily, the pattern from the previous diagram disappears and a new pattern is observed with two equal loops along the rope.
• Frequency is double that of the first figure, but now half the wavelength.
• This is because the distance from one node to another is = half a wavelength.
• Length of the rope is equal to one full wavelength
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What’s actually
happening?
• The red wave is reflected off the fixed end to become the blue wave.
• The green wave is the resultant (what we see)
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Comparing stationary waves & progressive waves
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What are harmonics? I
thought this was to do with music?
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Harmonics
• If a string is stretched between 2 points the points act as nodes.
• When the string is plucked a wave travels along the string and reflects off the end, creating two waves travelling in opposite directions.
• The wave vibrates in its fundamental mode and at the fundamental frequency, f0.
Wavelength is double the length of the string
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Higher harmonics• Since v=fλ, as
frequency increases wavelength will decrease.
• Shorter wavelengths will also fit exactly between the nodes.
• These are the harmonics where the frequency is an integer multiple of the fundamental frequency.
λ=2L/1
λ=2L/2
λ=2L/3
λ=2L/4
λ=2L/5
λ=2L/6
λ=2L/7
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How do Stationary waves behave in open &
closed tubes?
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Ever played the pan pipes?
• These pipes are closed at one end.
• Blowing across the top creates a stationary longitudinal wave inside which reflects off the bottom.
• The length of the pipe determines the wavelength of the wave.
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Representing sound waves
• Sound waves are longitudinal waves
– But they can still be represented graphically.
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Stationary sound waves
• Stationary waves can be represented as:
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Harmonics in closed tube sound waves
• For a stationary wave to form in a closed tube there must be a node at the closed end and an antinode at the open end.
• The wavelength is then determined by the length of the tube.
• Frequencies are always odd multiples of the fundamental frequency (3f0, 5f0, etc)
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Harmonics in open tube sound waves
• With open tubes, a standing wave must have an antinode at both ends.
• Harmonics are possible at all integer multiples of the fundamental wavelength.
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Practical
• Calculating the speed of sound in air using a resonance tube
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4.4.4 Stationary Waves (review)
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Complete!