PHYS 224 Introductory Physics III Spring 2008 Prof

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 1. html

Interacting Pulses from: http: //www. maths. gla. ac. uk/~fhg/waves 1. html

Interacting Pulses – same direction from: http: //www. maths. gla. ac. uk/~fhg/waves 1. html

Adding Traveling Waves from: http: //www. maths. gla. ac. uk/~fhg/waves 1. html

Adding Traveling Waves from: http: //www. maths. gla. ac. uk/~fhg/waves 1. html

Superposition of Simple Harmonic Motion Beat: Results from adding two harmonic oscillations with similar frequencies. Beat http: //www. kettering. edu/~drussell/Demos/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 = 15 dg qo = 60 dg 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

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#c 1

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/STS 066 -150 -074. htm