PHYS 224 - Introductory Physics III - Spring 2008

Prof. J. Vanderlei MartinsUMBC Department of Physics

Oscillations and Wavesfrom: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html

Interacting Pulsesfrom: 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 MotionBeat: 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

o = 60dgo = 15dg

Simple Pendulum Small angle approximation: sin() ~

How small is small?

http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html

Solutions:

Exact:

F = -mg•sin(

Approximation:

F = -mg•

Comparing Solutions:

Check the link below for simulations:http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html

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.

6.2

6.25

6.3

6.35

6.4

6.45

6.5

0 10 20 30 40 50

angle (dg)

Pe

rio

d (

s)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Re

lati

ve

Dif

fere

nc

e (

%)

Approximation Exact % Diff.

Comparing Solutions:F=-mg

xF = -mg sin()

Waves are the key to sound, color, and much more:

• Rainbow• Sunglint• Tsnunamis• Earthquakes• Cel Phone signals• Microwave ovens• Musical Instruments• …

http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/raibowcon.html#c1

Rainbow Physics

Cloud Rainbow observed from space:F-M. Breon, P. Goloub, 1998.

The Sunglint

• What is its connection with oscillations and waves?

Picture by Yoram Kaufman

Sunglint:Windy and Polluted Day

Sunglint:“Calm and Clean” Day

Picture by Yoram Kaufman

http://deathstar.rutgers.edu/projects/viewnj/pages/STS066-150-074.htm