1. Traveling Waves Coupled Harmonic Oscillator animation. Multiple Harmonic Oscillator animation. Wave Equation for String. Wave Equation solutions. Traveling Wave animation. Traveling Wave generation. Example problems Transverse and Longitudinal Waves Power in Traveling Wave

2. Coupled Harmonic Oscillator 2 Harmonic Oscillators coupled together http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/ CoupledSHM/CoupledSHM.html http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/ CoupledSHM/CoupledSHM.html Notice 2 rates: – Rate at which individual pendulums swing – Rate at which energy is transferred from one to other.

3. Multiple Coupled Harmonic Oscillator Multiple pendulums coupled together https://www.youtube.com/watch?v=sgwdhmsXcaU http://www.youtube.com/watch?v=V87VXA6gPuE webm (HTML5) files - should just play in any browser.

4. Coupled Harmonic Oscillator Summary Two observations – Each individual oscillator/pendulum has its own individual harmonic motion – A net disturbance is passed between oscillators at an entirely different rate. (Railcar analogy – motion of individual cars vs. coupling “wave” between cars as train first moves)

5. Wave Equation for String

6. Solutions for String Wave Equation v2v2

7. Traveling wave animation http://www.animations.physics.unsw.edu.au/jw/travelling_sine_wave.htm http://www.animations.physics.unsw.edu.au/waves-sound/travelling-wavesII In animation note: – Wavelength – Frequency

8. Traveling wave generation Traveling wave animation http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html Settings – No end – Zero damping – Oscillate Pause/Step/Advance through 1 cycle – Show Wavelength – Show Frequency – Show Velocity = wavelength * frequenc y

9. Frequency, wavelength, velocity

10. Examples 1

11. Examples 2

12. Examples 3

13. Transverse and Longitudinal Waves Transverse vs Longitudinal Waves http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/ long_wave.html http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/ long_wave.html Transverse – Waves on String Longitudinal – Sound Waves

14. Energy transport in wave

15. Energy spreading in spherical wave

16. Intensity/Amplitude variation with distance