Wave Physics PHYS2023phyweb.phys.soton.ac.uk/quantum/lectures/waves/waves20... · 2020. 11. 8. ·...
Transcript of Wave Physics PHYS2023phyweb.phys.soton.ac.uk/quantum/lectures/waves/waves20... · 2020. 11. 8. ·...
Wave PhysicsPHYS 2023
Tim Freegarde
12 Longitudinal waves2020-21
2
Wave Physics
WAVE EQUATIONS &
SINUSOIDAL SOLUTIONS
wave equations, derivations and solution
sinusoidal wave motions
complex wave functions
WAVE PROPAGATION
Huygens’ model of wave propagation
interference
general wave phenomena
Fraunhofer diffraction
longitudinal waves
BEHAVIOUR AT
INTERFACES
continuity conditions
boundary conditions
SUPERPOSITIONSlinearity and superpositions
Fourier series and transforms
FURTHER TOPICSwaves from moving sources
operators for waves and oscillations
waves in three dimensions
http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7
further phenomena and implications
3
Wave Physics
• a collective bulk disturbance in which what happens at any given position is a delayed response to the disturbance at adjacent points
Local/microscopic definition:
• speed of propagation is derived
• What is the net force on the penguin?
• For an elastic penguin, Hooke’s law gives
• If the penguin has mass , Newton’s law gives
• rest position
• displacement
• pressure
• elasticity
• density
• separation
• where
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Longitudinal waves
use physics/mechanics to write partial differential wave
equation for system
insert generic trial form of solution
find parameter values for which trial form is a solution
5
Longitudinal waves
ξ
x x+δx
use physics/mechanics to write partial differential wave
equation for system
insert generic trial form of solution
find parameter values for which trial form is a solution
rest
displaced
ξ+δξ
O
P Q
R
O
P′ Q′
RW(x)
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Sound waves
• in gases, use pressure difference
7
Speed of sound in air
8
Speed of sound in air
9
Sound waves
• wave equation:
where the elasticity
ratio of specific heats
ambient pressure
• wave velocity:
www.youtube.com/watch?v=52UAEQfMTtU
air
helium
SF6
1.40
1.66
1.10
0.167
6.26
1.205
1000
135
340
kg m-3 m s-1
metals
water 1500
4000
10
Visual microphone
https://www.youtube.com/watch?v=FKXOucXB4a8http://news.mit.edu/2014/algorithm-recovers-speech-from-vibrations-0804
11
Thermal waves (diffusion)
x x+δx
use physics/mechanics to write partial differential wave
equation for system
insert generic trial form of solution
find parameter values for which trial form is a solution
1 2
Q1 Q2
Q
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Thermal (diffusion) waves
13
Thermal (diffusion) waves
14
Traffic waves
Y Sugiyama et al., N J Phys 10, 033001 (2008)
• 22 vehicles on 230 m circumference
• requested to cruise at 30 kmh
• ‘jam’ propagates backwards at ~20 kmh
15
Wave Physics
WAVE EQUATIONS &
SINUSOIDAL SOLUTIONS
wave equations, derivations and solution
sinusoidal wave motions
complex wave functions
general wave phenomena
WAVE PROPAGATION
Huygens’ model of wave propagation
interference
Fraunhofer diffraction
longitudinal waves
BEHAVIOUR AT
INTERFACES
continuity conditions
boundary conditions
SUPERPOSITIONSlinearity and superpositions
Fourier series and transforms
http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7
FURTHER TOPICSwaves from moving sources
operators for waves and oscillations
waves in three dimensions
further phenomena and implications
Wave PhysicsPHYS 2023
Tim Freegarde