Wave Physics
PHYS 2023
Tim Freegarde
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
• energy in wave motions
2
Electromagnetic waves
• vertical component of force
• delay may be due to propagation speed of force (retarded potentials)
• electric field = force per unit charge (q2)
3
Sinusoidal waves
ω
z
• simple harmonic motion
• circular motion
where
4
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
~
 


5
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



6
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
7
Complex wave functions
yx, t   sin kx  t 
 Reexp ikx  t 
 Reexp i x, t 
φ
• simple harmonic motion
• circular motion
8
Dispersion in dissipative systems
y
2
 v
M x
W
yx,t0 
1
W
δx
x-δx
x
x+δx
x
9
Wave propagation
•
•
•
•
•
transverse motion of taut string
e-m waves along coaxial cable
shallow-water waves
flexure waves
string with friction
• travelling wave:
•
•
•
•
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
• string motion from initial conditions
find parameter values for
which trial form is a solution
10
Wave Physics
PHYS 2023
Tim Freegarde
Energy of waves on a string
h(x)
v
δy
δx
x
x
• kinetic:
• potential:
12
Velocities of waves on a string
x
x
• phase velocity
• (group velocity)
• transverse string velocity
13
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
14
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
15
Deep water waves
ε1
ε2
h(x)
volume = h(x) (δx+ε2-ε1) δy
v1
v2
δx
x-δx
x
x+δx
x
16
Deep water waves
h(x)
volume = h(x) (δx+ε2-ε1) δy
v1
δx
x-δx
x
x+δx
x
17
Water waves
theguardian.com
www.fluidconcept.co.uk/Images/Uploads/capetown1-400-279.jpg
• Ocean waves
• Severn bore
• Kelvin ship wake
• Tsunami
© Reuters / Mainichi Shimbun
© Jason Hawkes / Getty Images