Unit 1: Physics of Sound

Unit 1: Physics, Physiology, and Psychology of Sound

• Sine waves (sinusoids, pure tones): Things have mass, springiness, and are acted upon by force, creating simple harmonic motion. Amplitude (A or v) is the difference between two points (always positive). Frequency (f) determines period. Period (T) is the time to complete one repetition of a sine wave. Frequency and period are inversely related (1/period = frequency, 1/frequency = period).

Complex Waves

• Complex waves: Every sound signal is made up of pure tones, even complex ones. In-phase waves sum amplitudes; out-of-phase waves cancel out (e.g., noise-canceling technology). Fixed-phase waves (click train/pulse) have known starting phases. Random-phase waves (noise) have unknown starting phases, but have the same tones as a click train/pulse.

• Frequency spectrum: White noise has a flat frequency spectrum, meaning all frequencies are equally represented in a short time window. A sample over an infinitely long period also shows a flat spectrum. FFT (fast Fourier transform) converts a signal from the time domain (original signal variation over time) to the frequency domain (spectrum showing component frequencies).

Wave Types

• Longitudinal waves: Displacement of molecules is parallel to propagation (e.g., sound waves).
• Transverse waves: Propagation and displacement of molecules are perpendicular (e.g., earthquake waves).
• Surface waves: Combination of transverse and longitudinal waves (e.g., water waves) where molecules move in a circle .

Propagation

• Propagation: When sound encounters a new medium, it can be reflected, absorbed, or transmitted.

Reflection and Absorption

• Inverse square law: Sound intensity decreases as a function of distance. The function of friction and energy loss is dispersing more energy over a larger area.
• Monopole: Propagation expands in all directions.
• Dipole: Displacement occurs in one direction

Variables of Propagation

• Speed of sound and wavelength (λ) are related by a constant propagation speed. Frequency (f) is related to wavelength (λ) and speed of sound (v).

Wave Boundaries

• Fixed boundary: Theoretical; displacement remains zero, resulting in a 180-degree phase change and all reflected energy.
• Free boundary: Theoretical; no phase change, restoring force is zero, and more displacement in the new medium.

Decibels (dB)

• Decibel (dB): log-scale measurement of intensity; a change in 10 dB means a 10x change in intensity (Weber's Law).

Filters

• Filters: Change signal intensity across different frequencies. Low-pass filters attenuate high frequencies; High-pass filters attenuate low frequencies; Band-pass filters attenuate both high and low frequencies; Stopband filters attenuate a specific band.

Analog vs. Digital Signals

• Analog signals: Continuous in time and amplitude (e.g., record player, cassette).
• Digital signals: Discrete steps in time and amplitude; sampling converts analog signals to digital ones. Nyquist theorem—must sample at least twice the signal frequency to avoid losing information (aliasing).

Psychophysics: Thresholds, Laws and Theory

• Thresholds: Limits of detection obtained using methods of Limits, Adjustment, and Constant Stimuli; these may be influenced by sensitivity (sensory factors) and response bias (non-sensory factors). Signal Detection Theory separates sensory and non-sensory factors to properly estimate sensitivity.

• Weber's Law: The amount of change needed to detect a difference is proportional to the magnitude of the stimulus.

• Fechner's Law: Sensation is proportional to the logarithm of stimulus intensity.

Other Concepts

• Cochlear Implants (CIs): Electrical stimulation of auditory nerve to bypass inner/outer hair cells. CIs keep envelope and remove fine structure in sound. Current spread is a limitation as is frequency warping. Masking can also be an effect.
• Psychoacoustics: Study of physical and perceived sound, including sound localization (interaural time and level differences), and related terminology, like inverse square law, harmonic frequencies, and loudness recruitment. Tonotopy in the auditory nerve refers to the organization of neurons by frequency within the cochlea, and other auditory pathways.
• Frequency coding: Neural firing codes for frequency within the auditory nerve, with rate mechanism for low frequencies and place for higher frequencies. Volley theory is a coding mechanism which best explains neural firing for low frequencies.