PHYS 224 - Introductory
Physics III - Spring 2008
Prof. J. Vanderlei Martins
UMBC Department of Physics
Oscillations and Waves
from:
http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Interacting Pulses
from:
http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Interacting Pulses – same direction
from:
http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Adding Traveling Waves
from:
http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Adding Traveling Waves
from:
http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Superposition of Simple Harmonic Motion
Beat: Results from adding two harmonic oscillations with similar frequencies.
Beat
http://www.kettering.edu/~drussell/Demos/superposition/superposition.html
Lissajous Figures:
Number of tangents in each axes provides
information on the period ratio
Figure Credit:
http://en.wikipedia.org/wiki/Lissajous_curve
Simple Pendulum
Small angle approximation:
sin(q) ~ q
How small is small?
qo = 15dg
qo = 60dg
http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html
Solutions:
Exact:
Approximation:
Fq = -mg•sin(q)
Fq = -mg•q
Comparing Solutions:
Up to ~15 degrees initial displacement, the
small angle approximation holds well and
even after several oscillations the
approximate solution compares well with the
“exact” solution. For larger angles (e.g. the 60
dgs shown in the simulation, the approximate
solution diverges quickly from the “exact”
result.
Check the link below for simulations:
http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html
6.5
4.5
6.45
Comparing Solutions:
Fq=-mgq
x
Fq = -mg sin(q)
Period (s)
6.4
3.5
3
2.5
6.35
2
6.3
1.5
1
6.25
0.5
6.2
0
0
10
20
30
40
angle (dg)
Approximation
Exact
% Diff.
50
Relative Difference (%)
4
Waves are the key to sound, color,
and much more:
•
•
•
•
•
•
•
•
Rainbow
Sunglint
Tsnunamis
Earthquakes
Cel Phone signals
Microwave ovens
Musical Instruments
…
Rainbow Physics
http://hyperphysics.phyastr.gsu.edu/hbase/atmos/raibowcon.html#c1
Cloud Rainbow observed from space:
F-M. Breon, P. Goloub, 1998.
The Sunglint
• What is its connection with oscillations and
waves?
Sunglint:
Windy and Polluted Day
Picture by Yoram Kaufman
Sunglint:
“Calm and Clean” Day
Picture by Yoram Kaufman
http://deathstar.rutgers.edu/projects/viewnj/pages/STS066-150-074.htm