This material is based on work supported by the National Science Foundation under CCLI Grant DUE 0717743,
Jennifer Burg PI, Jason Romney, Co-PI.
2 Chapter 2 Sound Waves ...................................................................1
2.1 Concepts ...................................................................................1
2.1.1 Sound Waves, Sine Waves, and Harmonic Motion ................... 1
2.1.2 Properties of Sine Waves .....................................................5
2.1.3 Longitudinal and Transverse Waves ......................................8
2.1.4 Resonance .........................................................................9
2.1.4.1 Resonance as Harmonic Frequencies ..................................9
2.1.4.2 Resonance of a Transverse Wave .....................................10
2.1.4.3 Resonance of a Longitudinal Wave ...................................13
2.1.5 Digitizing Sound Waves .....................................................15
2.2 Applications .............................................................................15
2.2.1 Acoustics .........................................................................15
2.2.2 Sound Synthesis ...............................................................16
2.2.3 Sound Analysis .................................................................17
2.2.4 Frequency Components of Non-Sinusoidal Waves ................. 20
2.2.5 Frequency, Impulse, and Phase Response Graphs ................. 21
2.2.6 Ear Testing and Training ....................................................23
2.3 Science, Mathematics, and Algorithms ........................................24
2.3.1 Modeling Sound in Max ......................................................24
2.3.2 Modeling Sound Waves in Pure Data (PD) ............................ 27
2.3.3 Modeling Sound in MATLAB ................................................28
2.3.4 Reading and Writing WAV Files in MATLAB ........................... 36
2.3.5 Modeling Sound in Octave ..................................................37
2.3.6 Transforming from One Domain to Another .......................... 38
2.3.7 The Discrete Fourier Transfer and its Inverse ....................... 39
2.3.8 The Fast Fourier Transform (FFT) ........................................40
2.3.9 Applying the Fourier Transform in MATLAB ........................... 41
2.3.10 Windowing the FFT ...........................................................46
2.3.11 Windowing Functions to Eliminate Spectral Leakage .............. 48
2.3.12 Modeling Sound in C++ under Linux ...................................52
2.3.13 Modeling Sound in Java .....................................................54
2.4 References ..............................................................................59
2 Chapter 2 Sound Waves
2.1 Concepts
2.1.1 Sound Waves, Sine Waves, and Harmonic Motion
Working with digital sound begins with an understanding of sound as a physical phenomenon.
The sounds we hear are the result of vibrations of objects for example, the human vocal chords,
or the metal strings and wooden body of a guitar. In general, without the influence of a specific
sound vibration, air molecules move around randomly. A vibrating object pushes against the
randomly-moving air molecules in the vicinity of the vibrating object, causing them first to
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