Acoustics of Musical Instruments (eBook)

Part I - Basic Equations and Oscillators.- 1. Continuous models. 1.1 Strings, membranes, bars, plates and shells. 1.2 3D acoustic waves. 1.3 Energy, intensity, power.- 2. Single-degree-of-freedom oscillator. 2.1 Introduction. 2.2 Solution with and without a source. Green's function. 2.3 Examples of free and forced oscillations.- Part II - Waves and modes.- 3. Modes. 3.1 Introduction. 3.2 Time scale. Transition from wave to mode. 3.3 Definitions and basic properties of the eigenmodes.- 4. Waves. 4.1 Introduction. 4.2 Solutions without source, first reflection. 4.3 Successive reflections of waves produced by a pulse source.- 5. Dissipation and damping. 5.1 Introduction: dissipative phenomena in musical acoustics. 5.2 Generalizing the concept of mode. 5.3 Damping mechanisms in solid materials.- 6. Coupled systems. 6.1 Introduction. 6.2 Structure-cavity interaction. 6.3 Coupling of piano strings.- 7. Wind Instruments: variable cross section and toneholes. 7.1 Introduction. 7.2 Pipes with variable cross section: general equations. 7.3 Pipes with cross section discontinuities: first approximation.- Part III - Nonlinearities and self-oscillations.- 8. Nonlinearities. 8.1 An example of asymmetry: the interrupted pendulum. 8.2 Duffing equation. 8.3 Nonlinear vibration of strings.- 9. Reed instruments. 9.1 Background on self-sustained oscillations. 9.2 Reed-instruments models. 9.3 Behavior of the two-equation model (regimes, existence and stability, transients) without reed dynamics.- 10. Flute-like instruments. 10.1 An introduction and general description. 10.2 A global model for the instrument. 10.3 A modeling for the jet oscillation.- 11. Bowed string instruments. 11.1 Introduction. 11.2 Bow-string interaction. 11.3 Bow models.- Part IV - Radiation and sound-structure interaction. - 12. Elementary sources and multipoles. 12.1 Introduction: acoustical radiation of musical instruments. 12.2 Elementary sources. 12.3 Pulsating sphere.- 13. Radiation of vibrating structures. 13.1 Introduction. 13.2 Basic concepts in structural acoustics. 13.3 Radiation of an infinite thin plate.- 14. Radiation of complex systems. 14.1 Example of the vibraphone. 14.2 Example of the kettledrum. 14.3 Example of the guitar.- Glossary.- Index.