Transcript Wave Physics PHYS2023 - Physics and Astronomy Southampton

Wave Physics
PHYS 2023
Tim Freegarde
Coming up in Wave Physics...
• local and macroscopic definitions of a wave
• transverse waves on a string:
• wave equation
• travelling wave solutions
• other wave systems:
• electromagnetic waves in coaxial cables
• shallow-water gravity waves
• sinusoidal and complex exponential waveforms
2
Wave equations
• waves are collective bulk disturbances, whereby the
motion at one position is a delayed response to the
motion at neighbouring points
• propagation is defined by differential equations,
determined by the physics of the system, relating
derivatives with respect to time and position
use physics/mechanics to
write partial differential wave
equation for system
insert generic trial form of
solution
e.g.
• but note that not all wave equations are of the same
form
find parameter values for
which trial form is a solution
3
Solving the wave equation
• shallow waves on a long thin flexible string
• travelling wave
• wave velocity
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
4
So far in Wave Physics...
• local and macroscopic definitions of a wave
• transverse waves on a string:
• wave equation
• travelling wave solutions
• other wave systems:
• electromagnetic waves in coaxial cables
• shallow-water gravity waves
• sinusoidal and complex exponential waveforms
5
Deep water waves
ε1
ε2
h(x)
volume = h(x) (δx+ε2-ε1) δy
   
dh
 h 2 1
dt
x
v1
v2
δx
x-δx
x
x+δx
x
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Deep water waves
h(x)
volume = h(x) (δx+ε2-ε1) δy
   
dh
 h 2 1
dt
x
h  h 
dv1
 g 2 1
dt
x
v1
δx
x-δx
x
x+δx
x
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Coming up in Wave Physics...
• today’s lecture:
• local and macroscopic definitions of a wave
• transverse waves on a string:
• wave equation
• travelling wave solutions
• other wave systems:
• electromagnetic waves in coaxial cables
• shallow-water gravity waves
• sinusoidal and complex exponential waveforms
8
Electromagnetic waves
• vertical component of force
• delay may be due to propagation speed of force (retarded potentials)
• electric field = force per unit charge (q2)
9
Sinusoidal waves
ω
z
• simple harmonic motion
• circular motion
where
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Sinusoidal waves
• occur when source is rotating or performing SHM
• detected by resonant detectors
• conveniently manipulated in differential equations
• allow standing wave solutions
• only real travelling wave solutions in dispersive systems
• useful terminology for dissipative systems
• complete set of orthogonal solutions in linear systems
• convenient for energy/power calculations
11
Sinusoidal waves
y
t  t0
x
yx, t   y0 sin t  kx   
at

t  t0 ,
yx, t0   y0 sin  kx    t0 
 y0 sin  2 ~ x    t0 
 2

 y0 sin  
x    t0 
 

• wavenumber
• spectroscopists’
wavenumber
• wavelength
k
2

1
~
 


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Sinusoidal waves
y
x  x0
t
yx, t   y0 sin t  kx   
at

x  x0 ,
yx0 , t   y0 sin t    kx0 
• angular frequency
 y0 sin 2  t    kx0 
• frequency
 2

 y0 sin  t    kx0 
 

• period

2

1



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Velocities of waves on a string
x
x
• phase velocity
• (group velocity)
• transverse string velocity
14
Energies of waves on a string
δy
δx
x
x
• kinetic:
• potential:
15
Sumatra-Andaman earthquake 2004
26 Dec 2004
•
•
•
•
•
magnitude 9.15; 275,000 perished
1200 km along India/Burma plate subduction zone
slip of 15 m sideways, several metres vertically
formed ridges 1.5 km high, trench kms wide
30 km3 water displaced
Tsunami Inundation Mapping Efforts
NOAA/PMEL - UW/JISAO
16
Sumatra-Andaman earthquake 2004
•
•
•
•
•
magnitude 9.15; 275,000 perished
1200 km along India/Burma plate subduction zone
slip of 15 m sideways, several metres vertically
formed ridges 1.5 km high, trench kms wide
30 km3 water displaced
• ocean waves ~ 60 cm
• 25 m high near shore
NOAA
17