1. Nonlinear Acoustics and Applications Doug Pinckney

2. Background Acoustics Definition Sound – Pressure fluctuations through a medium, propagate at the speed of sound Well approximated by linear models at low amplitudes

3. Nonlinearities

4. Why Do We Care As it turns out, most sound we hear every day is linear, however… Astounding Applications – Ultrasound – Sonic Boom – Acoustic levitation – Harmony and Music

5. Medical Imaging (Ultrasound) Different fluids in the body have different densities – Must be understood using nonlinear models to create an accurate image Additionally, harmonic structure of nonlinear waves

6. Sonic Boom Objects traveling through fluid cause pressure changes (high in front, low in back) If objects go supersonic, these waves merge to form an “N-Wave” “Boom” caused by sharp change in pressure

7. Importance Nonlinear acoustics are required for understanding Of great interest to engineers for construction of supersonic craft – Craft failure – Ground damage

8. Acoustic Levitation First observed: Kundt’s Tube experiment (1866) Setup:

9. Advancements/Applications Original experiments done with linear sound – Effects amplified greatly with high amplitude, nonlinear sound Applications – Manufacturing: Spheres Container-less work Foam research

10. Music Negative resistance allows for sustained tones – Arises from nonlinear inputs

11. Harmony In a perfect world, harmony arises from the interaction of frequencies that are an integer multiple of each other In reality, exact frequencies are near impossible (clarinet, violin) Nonlinearities in frequencies near harmonics converge to harmony

12. Proposal To further investigate the practical applications of nonlinear acoustics, focusing on: – Acoustic levitation – Sonic Boom – Music

13. Questions?

14. References Nonlinear Dynamics and Chaos in Musical Instruments- NH Fletcher The Feynman Lectures, 50 “Harmonics”- Richard Feynman http://science.howstuffworks.com/acoustic- levitation.htm A Standing Wave Acoustic Levitation System for Large Planar Objects- S. Zhao and J. Wallaschek Sonic Boom Propagation Revisited: A Nonlinear Geometrical Acoustic Model- M. Berci and L. Vigevano