Traveling Waves Coupled Harmonic Oscillator animation. Multiple Harmonic Oscillator animation. Wave Equation for String. Wave Equation solutions. Traveling.

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Presentation transcript:

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

Coupled Harmonic Oscillator 2 Harmonic Oscillators coupled together CoupledSHM/CoupledSHM.html CoupledSHM/CoupledSHM.html Notice 2 rates: – Rate at which individual pendulums swing – Rate at which energy is transferred from one to other.

Multiple Coupled Harmonic Oscillator Multiple pendulums coupled together webm (HTML5) files - should just play in any browser.

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)

Wave Equation for String

Solutions for String Wave Equation v2v2

Traveling wave animation In animation note: – Wavelength – Frequency

Traveling wave generation Traveling wave animation Settings – No end – Zero damping – Oscillate Pause/Step/Advance through 1 cycle – Show Wavelength – Show Frequency – Show Velocity = wavelength * frequenc y

Frequency, wavelength, velocity

Examples 1

Examples 2

Examples 3

Transverse and Longitudinal Waves Transverse vs Longitudinal Waves long_wave.html long_wave.html Transverse – Waves on String Longitudinal – Sound Waves

Energy transport in wave

Energy spreading in spherical wave

Intensity/Amplitude variation with distance