350 Week 1 Acoustic Phonetics and Sound Wave Mechanics

Fundamentals of Sound Production and Transmission

• Sound is created by an audible disturbance, or wave, in a medium caused by a vibrating source.

• Primary examples of sound sources include:

  • Tuning forks

  • Vocal folds

• Sound propagates through physical mediums existing in different states of matter:

  • Gas

  • Liquid

  • Solid

• Speech is most usually transmitted through air.

• Sound at its fundamental level consists of physical vibrations.

Pure Tones and Simple Harmonic Motion

• A pure tone is an acoustic signal that consists of only one single frequency.

• Fundamental periodic definitions:

  • Cycle: A single complete back-and-forth vibration of a wave.

  • Frequency of vibration: The number of completed cycles within a time period of one second ($1\,s$).

• Tuning forks serve as a standard physical example of a pure tone generator executing simple harmonic motion.

• Progression of simple harmonic motion (SHM):

  • Rest position ($A$): Initial equilibrium state.

  • Force applied: Induces displacement to position $B$

  • Elasticity (restoring force): Drives the object back to rest position $A$

  • Inertia: The physical tendency for motion or lack of motion to continue, which drives the object past rest position $A$ to displacement position $C$

  • Elasticity (restoring force): Drives the object back to rest position $A$

• Dynamic physical properties across displacement positions:

  • Position A: Has maximum velocity: the speed of an object.

  • Positions B and C: Has zero velocity, maximum displacement, and maximum acceleration: the rate of change in velocity.

Waveform Parameters: Amplitude, Damping, Compression, and Rarefaction

• B, D, F, H, J, L: Zero velocity, maximum acceleration

• C, E, G, I, K: Maximum velocity

  • A not included because object starts at rest.

• Amplitude and energy reduction:

  • Amplitude: The absolute extent or magnitude of physical motion of the vibrating body.

  • Damping: The progressive decrease in the amplitude of displacement over time due to friction or air resistance.

• Atmospheric sound wave propagation mechanics:

  • Compression: A region in an acoustic wave where air molecules are packed closely together, creating high air pressure.

  • Rarefaction: A region in an acoustic wave where air molecules are spread farther apart, creating low air pressure.

• Phase transitions in longitudinal pressure waves:

  • State at rest $\rightarrow$ Compression phase $\rightarrow$ Rarefaction phase.

Complex Tones and Fourier Frequency Spectra

• Principles of complex tones:

  • A complex tone is a composite sound created by combining two or more pure tone frequencies.

  • Pure tone component frequency summation example:

  • Pure tone component 1: $100\,Hz$

  • Pure tone component 2: $200\,Hz$

  • Pure tone component 3: $300\,Hz$

  • The summation of component pure tones produces a complex periodic wave across time ($0.00\,s$ to $0.02\,s$).

• Frequency domain representation:

  • Waveform domain: Displays amplitude variations plotted continuously over time in seconds ($s$).

  • Spectrum domain: Displays discrete pure tone components by plotting amplitude against frequency in Hertz ($Hz$).

  • The spectrum of the sum wave displays discrete vertical lines at each fundamental component frequency, specifically at $100\,Hz$, $200\,Hz$, and $300\,Hz$.