Transcript Wave Physics PHYS2023

Wave Physics
PHYS 2023
Tim Freegarde
Thermal waves (diffusion)
1
2
use physics/mechanics to
write partial differential wave
equation for system
W
insert generic trial form of
solution
W1
W2
x
find parameter values for
which trial form is a solution
x+δx
2
Sumatra-Andaman earthquake 2004
26 DEC 2004 04:15Z
===================
FROM: UN ENVOY SUMATRA
TO:
CHIEF SCI ADVISOR LONDON
MAGNITUDE 9.1 EARTHQUAKE ALONG
INDIA-BURMA SUBDUCTION ZONE.
1200KM FAULT LEAVING KM-WIDE
RIDGES AND TROUGHS.
30 CUBIC-KM WATER DISPLACED.
NOAA SATELLITE RADAR REPORTS
+2HRS WAVE HEIGHT 0.6M
+3HRS WAVE HEIGHT 0.4M
PLS ADVISE ++ UTMOST URGENCY ++
Tsunami Inundation Mapping Efforts
NOAA/PMEL - UW/JISAO
3
Sumatra-Andaman earthquake 2004
26 DEC 2004 04:15Z
===================
FROM: UN ENVOY SUMATRA
TO:
CHIEF SCI ADVISOR LONDON
MAGNITUDE 9.1 EARTHQUAKE ALONG
INDIA-BURMA SUBDUCTION ZONE.
1200KM FAULT LEAVING KM-WIDE
RIDGES AND TROUGHS.
30 CUBIC-KM WATER DISPLACED.
NOAA SATELLITE RADAR REPORTS
+2HRS WAVE HEIGHT 0.6M
+3HRS WAVE HEIGHT 0.4M
PLS ADVISE ++ UTMOST URGENCY ++
•Seychelles
•Maldives
•Mauritius/Reunion
Uwe Dedering / Wikipedia Commons
4
Sumatra-Andaman earthquake 2004
•Seychelles
•Maldives
•Mauritius/Reunion
UN Office for the Coordination of Human Affairs
Uwe Dedering / Wikipedia Commons
5
Sumatra-Andaman earthquake 2004
UN Office for the Coordination of Human Affairs
Tsunami Inundation Mapping Efforts
NOAA/PMEL - UW/JISAO
• NOAA radar was experimental
• data analysis and wave simulation were not possible until days later
• 275,000 people perished
6
Wave Physics
general wave phenomena
WAVE EQUATIONS &
SINUSOIDAL SOLUTIONS
wave equations, derivations and solution
sinusoidal wave motions
complex wave functions
Huygens’ model of wave propagation
WAVE PROPAGATION
interference
Fraunhofer diffraction
longitudinal waves
BEHAVIOUR AT
INTERFACES
SUPERPOSITIONS
continuity conditions
boundary conditions
linearity and superpositions
Fourier series and transforms
waves in three dimensions
FURTHER TOPICS
waves from moving sources
operators for waves and oscillations
further phenomena and implications
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http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7
Wave propagation
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transverse motion of taut string
e-m waves along coaxial cable
shallow-water waves
flexure waves
string with friction
• travelling wave:
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general form
sinusoidal
complex exponential
damped
use physics/mechanics to
write partial differential wave
equation for system
insert generic trial form of
solution
• standing wave
• soliton
•
•
•
•
•
speed of propagation
dispersion relation
Huygens reflection, refraction and diffraction
reflection and transmission at interfaces
string motion from initial conditions
find parameter values for
which trial form is a solution
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A frayed guitar string
ψ
2
M2
1
yx,t0 
M1
W
W
δx
x-δx
x
x+δx
x
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Reflection at an interface
combine forward and
reflected waves to give total
fields for each region
apply continuity conditions
for separate components
y
A
B
x
hence derive fractional
transmission and reflection
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Continuity conditions
• for a boundary at
between regions A and B:
• transverse waves on a string:
• electromagnetic waves:
non-normal incidence:
• sound waves:
• thermal waves:
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Significance of continuity conditions
• various derivations and forms
• typically: • one condition derived from balance of forces
• conservation of momentum
• the two conditions combined
• conservation of energy
Transverse waves on a string
• energy density:
•  power:
where
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Energy of waves on a string
h(x)
v
δy
δx
x
x
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Impedance
• at interface between two media:
• transverse waves on a string:
• electromagnetic waves:
• sound waves:
• thermal waves:
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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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