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SI 2008: Study of Wave Motion

July 19, 2008 Martin Bobb Joseph Marmerstein Feibi Yuan Caden Ohlwiler. SI 2008: Study of Wave Motion. Introduction. Goal -- Model Motion of Waves MATLAB -- Programming Application Method Approximating the Wave Equation. MATLAB. Software with simulation and visualization functions

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SI 2008: Study of Wave Motion

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  1. July 19, 2008 Martin Bobb Joseph Marmerstein Feibi Yuan Caden Ohlwiler SI 2008: Study of Wave Motion

  2. Introduction • Goal -- Model Motion of Waves • MATLAB -- Programming Application • Method • Approximating the Wave Equation

  3. MATLAB • Software with simulation and visualization functions • “Matrix Laboratory” • Uses matrices to perform complex calculations • Most of our group has limited programming experience • No previous MATLAB experience

  4. Wave Equation • This is a partial differential equation (college level math) • Continuous • Approximated using the Finite Difference Method

  5. Boundary Conditions • Behavior at the edges of the simulation • Fixed • Out of phase reflection • Free • In phase reflection • No-reflection boundaries are very difficult

  6. Two Dimensional Waves • Wave in x-y plane • Like the surface of a lake • Third dimension represents wave height • Set conditions to represent air • Wave propagation speed • Viscosity • Nyquist frequency • Highest frequency that can be resolved accurately • Simulation must run at twice that • 22100 Hz

  7. Initial Disturbances and Forcing Functions • Initial disturbance • One disturbance, dissipates over time (much like a shock wave) • Forcing Function • Continuous Output • Similar to a speaker playing a single note • Follows the path of a sine wave

  8. Initial Disturbance

  9. Forcing Function

  10. Viscosity • Viscosity • Measure of the resistance to motion from a fluid • Adds a new term to wave equation • Makes the wave equation more realistic • Molasses vs. Water

  11. Low Viscosity

  12. High Viscosity

  13. Virtual Throat Simulation • Two walls, space in between • Three microphones • Behind, inside and in front of the throat • Forcing function • 20 Hz

  14. Virtual Throat Visualization

  15. Fast Fourier Transforms (FFTs) • Fourier Transform • Mathematical method • Takes a function in time and changes it to frequency components • Shows the frequencies at which a system is responding • Fast Fourier Transform • Numerical method • Computes the Fourier Transform quickly

  16. FFT On Microphone #1 Relative Magnitude Frequency (Hz)‏

  17. FFT on Microphone #2 Relative Magnitude Frequency (Hz)‏

  18. FFT on Microphone #3 Relative Magnitude Frequency (Hz)‏

  19. Virtual Room Simulation Based on geometry of BALE Gallery room Forcing Function of 110 Hz “A” string on a guitar Three microphones Behind column, in front of column, behind “speakers” Simulation was not entirely successful Solution tends to “ring”

  20. Virtual Room Visualization

  21. Three Dimensional Waves • Volume divided into finite pieces • Wave “height” represents compression instead of actual wave height • Requires more computing power • Simulations take more time • Can take hours • Waves dissipate much faster than in 2D • Forcing functions have a less noticeable effect

  22. Three Dimensional Visualization • Tried multiple techniques in MATLAB • Isosurfaces • Generates meshes at specific wave heights • Did not provide relevant visual • Volume Rendering • Passes light through the simulation • Used in 3D visualizations • Alpha mapping • Does not display wave heights close to zero • Makes them transparent • White space isn’t necessarily motionless

  23. 3D Waves from Single Initial Disturbance

  24. Corner Disturbance

  25. Conclusions • Learned about wave motion • Computer simulations are difficult to make exact • Everything is approximated • Learned how to program in MATLAB • Learned about simulation and visualization • Learned how to use Linux

  26. Acknowledgments • Troy Baer -- Project Leader • Armen Ezekielian -- MATLAB support • Elaine Pritchard -- Food/snacks/organization • Daniel & Brianna -- Dorm supervisors • All the staff that gave presentations • James Rader -- Gallery blueprints • Third-party MATLAB add-ons: • Blinkdagger.com – positiveFFT function • Mathworks.com -- vol3d function

  27. 8 Disturbances

  28. 3D Waves from Two Initial Disturbances

  29. Questions?

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