Teaching Physics of Sound - Dmitry Garanin

Physics of Sound: PHY140/141

The course is accompanied by demonstrations using computer-based sound production & recording.
Sound production: Wolfram Mathematica
Sound recording: External USB soundcard with built-in microphones, wave editors

1. Introduction. Oscillations -

Definitions of physical quantities and units. Sound: Oscillations and waves. Simple harmonic oscillatons. Amplitude, period, and frequency (pitch). Harmonic oscillations with slowly changing parameters. Perception of sound. Anharmonic oscillations. Combinations of harmonic oscillations. Beats. Phase relations and phychoacoustical Ohm's law, phase beats. Damped and driven oscillations, resonance.

Problems: Berg & Stork, Ch.1: Questions: 5,7; Problems: 1,4.

2. Waves and Sound -

Plane waves: Periodic waves, solitary waves, wave packets. Wave length, sound velocity.

Spherical and cylindrical waves. Wave intensity; Inverse square law etc. Longitudinal and transverse waves. Polarization of transverse waves. Surface acoustic waves. Reflection and refraction of waves. Refraction of sound in the atmosphere. Interference of plane waves. Interference of spherical waves. Doppler effect. Sonic booms and shock waves.

Problems: Berg & Stork, Ch.2: Questions: 6,9; Problems: 2,7.

Demonstrations: Interference of two spherical waves | Doppler-effect | Longitudinal and transverse waves

3. Standing Waves and Overtone Series -

Standing waves in general. Role of boundary conditions in the formation of standing waves. Node-node, antinode-antinode, and node-antinode boundary conditions. Overtones series. Mersenne's laws.

Problems: Berg & Stork, Ch.3: Questions: 4,6,7; Problems: 3,5.

Demonstrations: Standing waves | Standing waves with node-node boundary conditions

4. Analysis and Synthesis of Complex Waves -

Synthesis of complex waves. Fourier analysis and Fourier spectra. Analysis of tone quality: Attacks and decays, formants. Vibrato and tremolo. Discrete and continuous Fourier spectra. Spectrograms: Narrow-band and wide-band.

Demonstrations: Square wave | Tremolo and Vibrato

Problems: Berg & Stork, Ch.4: Questions: 2,3,7; Problems: 1,2.

5. Resonances in Sound Production -

Role of resonances: Amplification of sound, shaping of sound (selection of particular frequency ranges), creation of sound in whistles and woodwind instruments. Helmholtz resonator and other resonators. Noise: White noise, colored noise. Filtering of noise by a resonator.

Problems: Berg & Stork, Ch.4: Questions: 8,9,10; Problems: 3,5.

6. Speech and singing -

Structure of speech and singing apparatus. Throat and mouth as a resonator. Naive open-closed-pipe theory of the throat-mouth resonator. Resonances as formants in shaping the output sound. Production of the glottal wave by the vocal folds, Bernoulli law. Difference between singing, speech, and hoarse speech. Simplified two-formant sinthesis of vowels.

Problems: Berg & Stork, Ch.6: Questions: 10,11,12.

7. Hearing -

Structure of the ear. Transmission of the signal through the ear parts. Place theory of hearing: Frequency response and frequency resolution. Physical sound intensity, amplitude and the intensity of the sound.. Sensitivity of the ear to the sound intensity. Logarithms. The decibel scale of sound intensity level. Decibels and phones. Nonlinearity of the ear. Aural harmonics. Combinational tones. Fundamental tracking. Masking. Binaural effects. Cochlear implants as a confirmation of the place theory of hearing.

Problems: Berg & Stork, Ch.6: Questions: 2,3,5; Problems: 1,2,3.

8. Room and auditorium acoustics -

Direct and reflected sound. Texture of the echo. Definition of the reverberation time. Fullness and clarity. Warmth and brilliance. Formula for the reverberation time. Absorption and reflection coefficients. Resonances in room of a box. shape. General principles of constructing concert halls.

9. Sound recording and reproduction -

History of sound recording. Acoustic vs electric recording. Phonograps. Vinyl records. Magnetic tape recorders. Digital recording. DAT and MiniDisc. CDs and their successors. Computer-based recording. Flash recorders. Legal problems with digital recordings. MIDI vs sound recording. Modern recording setup. Microphons: Dynamic and electret condenser microphons, polar pattern, frequency response. Preamplifiers and A/D converters.

10. Digital recording -

Discretization of the wave form. Sampling frequency. Sample depth (bit depth). CD vs high-resolution audio. Dynamic range. Bit rate and file size. Bits and bytes. Storage requirements. Internet delivery of digital music. Transfer rate. Audio compression. Lossless and lossy encoding. MP3 and other lossy encoding formats. Constant, variable, and average bit rate.

Problems

11. Music temperament -

Music sounds, notes. Pitch vs. interval. Phychological role of intervals. Temperaments. Overtone series and perfect intervals. Music scales (keys). Impossibility of a temperament using all perfect intervals. Open and close temperaments. Unequal and equal temperaments. Definition of the equal temperament. Frequency ratios in the equal temperament. Comparing wave forms of perfect and imperfect intervals. Pythagorean temperament as the simplest and historically first temperament. Wolf fifth and other problems of the Pythagorean temperament.

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