The Physics of Musical Instruments - Softcover

Inhaltsangabe

I Vibrating Systems.- 1 Free and Forced Vibrations of Simple Systems.- 1.1. Simple Harmonic Motion in One Dimension.- 1.2. Complex Amplitudes.- 1.3. Superposition of Two Harmonic Motions in One Dimension.- 1.4. Energy.- 1.5. Damped Oscillations.- 1.6. Other Simple Vibrating Systems.- 1.7. Forced Oscillations.- 1.8. Transient Response of an Oscillator.- 1.9. Two-Dimensional Harmonic Oscillator.- 1.10. Graphical Representations of Vibrations: Lissajous Figures.- 1.11. Normal Modes of Two-Mass Systems.- 1.12. Nonlinear Vibrations of a Simple System.- A.1. Alternative Ways of Expressing Harmonic Motion.- A.2. Equivalent Electrical Circuit for a Simple Oscillator.- References.- 2 Continuous Systems in One Dimension: Strings and Bars.- 2.1. Linear Array of Oscillators.- 2.2. Transverse Wave Equation for a String.- 2.3. General Solution of the Wave Equation: Traveling Waves.- 2.4. Reflection at Fixed and Free Ends.- 2.5. Simple Harmonic Solutions to the Wave Equation.- 2.6. Standing Waves.- 2.7. Energy of a Vibrating String.- 2.8. Plucked String: Time and Frequency Analyses.- 2.9. Struck String.- 2.10. Bowed String.- 2.11. Driven String: Impedance.- 2.12. Motion of the End Supports.- 2.13. Damping.- 2.14. Longitudinal Vibrations of a String or Thin Bar.- 2.15. Bending Waves in a Bar.- 2.16. Bars with Fixed and Free Ends.- 2.17. Vibrations of Thick Bars: Rotary Inertia and Shear Deformation.- 2.18. Vibrations of a Stiff String.- 2.19. Dispersion in Stiff and Loaded Strings: Cutoff Frequency.- 2.20. Torsional Vibrations of a Bar.- References.- 3 Two-Dimensional Systems: Membranes and Plates.- 3.1. Wave Equation for a Rectangular Membrane.- 3.2. Square Membranes: Degeneracy.- 3.3. Circular Membranes.- 3.4. Real Membranes: Stiffness and Air Loading.- 3.5. Waves in a Thin Plate.- 3.6. Circular Plates.- 3.7. Elliptical Plates.- 3.8. Rectangular Plates.- 3.9. Square Plates.- 3.10. Square and Rectangular Plates with Clamped Edges.- 3.11. Rectangular Wood Plates.- 3.12. Bending Stiffness in a Membrane.- 3.13. Shallow Spherical Shells.- 3.14. Nonlinear Vibrations in Plates and Shallow Shells.- 3.15. Driving Point Impedance.- References.- 4 Coupled Vibrating Systems.- 4.1. Coupling Between Two Identical Vibrators.- 4.2. Normal Modes.- 4.3. Weak and Strong Coupling.- 4.4. Forced Vibrations.- 4.5. Coupled Electrical Circuits.- 4.6. Forced Vibration of a Two-Mass System.- 4.7. Systems with Many Masses.- 4.8. Graphical Representation of Frequency Response Functions.- 4.9. Vibrating String Coupled to a Soundboard.- 4.10. Two Strings Coupled by a Bridge.- A.1. Structural Dynamics and Frequency Response Functions.- A.2. Modal Analysis.- A.3. Finite Element Analysis.- References.- 5 Nonlinear Systems.- 5.1. A General Method of Solution.- 5.2. Illustrative Examples.- 5.3. The Self-Excited Oscillator.- 5.4. Multimode Systems.- 5.5. Mode Locking in Self-Excited Systems.- References.- II Sound Waves.- 6 Sound Waves in Air.- 6.1. Plane Waves.- 6.2. Spherical Waves.- 6.3. Sound Pressure Level and Intensity.- 6.4. Reflection, Diffraction, and Absorption.- 6.5. Acoustic Components at Low Frequencies.- References.- 7 Sound Radiation.- 7.1. Simple Multipole Sources.- 7.2. Pairs of Point Sources.- 7.3. Arrays of Point Sources.- 7.4. Radiation from a Spherical Source.- 7.5. Line Sources.- 7.6. Radiation from a Plane Source in a Baffle.- 7.7. Unbaffled Radiators.- References.- 8 Pipes and Horns.- 8.1. Infinite Cylindrical Pipes.- 8.2. Wall Losses.- 8.3. Finite Cylindrical Pipes.- 8.4. Radiation from a Pipe.- 8.5. Impedance Curves.- 8.6. Horns.- 8.7. Finite Conical and Exponential Horns.- 8.8. Bessel Horns.- 8.9. Compound Horns.- 8.10. Perturbations.- 8.11. Numerical Calculations.- 8.12. The Time Domain.- References.- III String Instruments.- 9 Guitars and Lutes.- 9.1. Design and Construction of Guitars.- 9.2. The Guitar as a System of Coupled Vibrators.- 9.3. Force Exerted by the String.- 9.4. Modes of Vibration of Component Parts.- 9.5. Coupling of the Top Plate t

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