Transcript courses:lecture:wvlec:basic_wavefunctions_space_wiki.ppt

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BASIC WAVE CONCEPTS
Reading:
Main 9.0, 9.1, 9.3
GEM 9.1.1, 9.1.2
Knight Ch 20
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REVIEW SINGLE OSCILLATOR:
The oscillation functions you are used to describe how one
quantity (position, charge, electric field, anything ...)
changes with a single variable, TIME.
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At a FIXED POSITION in space, y (t) = A cos(wt + f )
2p
1
period T =
=
w f
A
1
position
y
-0.25
-A
0.25
0.75
-1

t

time
1.25
1.75
Oscillations in time
y (t) = A cos(wt + f )
2
1
T


f
(Cyclic) frequency, f (or n), dimension: [time-1]
Angular frequency, , dimension: [time-1]
Period, T, dimension: [time]
Amplitude A, or y0, dimension: [whatever]
Phase, t+, dimensionless
Phase constant, , dimensionless
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Equivalent representations …….
y(t) = Acos(wt + f )
y(t) = Bp cos(wt ) + Bq sin(wt )
i(wt )
-i(wt )
y(t) = Ce + C *e
iwt
y(t) = Re[ De ]
Remember the conversions between A, B, C, D
forms - see Main Ch. 1.
y (x) = A cos(kx + f )
At a FIXED TIME,
wavelength
1
A
2p
l=
k
A
position
y y
-0.25
-A
-1
0.25
0.75
-A
space
time
1.25
1.75
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Periodic variations in space
y(x) = Acos( kx + f )
2p
l=
k
Wave "vector", k, dimension: [length-1]
(wave number is 1/l)
Wavelength, l, dimension: [length]
Amplitude A, or y0, dimension: [whatever]
Phase, kx+, dimensionless
Phase constant, , dimensionless
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Equivalent representations …….
y (t)  A cos kx +  
y (t)  Bp cos kx  + Bq sin kx 
y (t)  Ce
i kx 
+ C *e
i kx 
y (t)  Re  Deikx 
Remember the conversions between A, B, C, D
forms - see Main Ch. 1.
If we have SEVERAL oscillators at different positions, we
can describe the variation of that same quantity (call it y) by
a function of TWO variables: TIME, just like before, and
another variable, POSITION, which identifies the location of
the oscillator.
Watch the animation. What can you say about the amplitude,
frequency and phase of each oscillator? Which direction does
each oscillator travel? Which way does the wave travel?
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Waves - functions of space AND time
Looking ahead….
We will discuss mostly harmonic waves where
variations are sinusoidal.
Pulses and non-harmonic waves are
superpositions of harmonic waves
Traveling and standing waves
Damped, (driven) waves
Reflection, transmission, impedance
Classical and quantum systems