Complex Waves

Principle of Superposition

When multiple waves overlap, resulting wave is sum of their displacements

Constructive Interference

Waves in phase add up, increasing amplitude

Destructive Interference

Waves out of phase cancel each other

Complex Wave

Combination of multiple sine waves

Harmonics

Integer multiples of a fundamental frequency

Contribute to voice quality and timbre (essential for speech production)

Source Filter Model

Explains how vocal fold vibrations generate harmonics, which are shaped by the vocal tract to produce speech sounds

Partials

Frequency components of a complex sound

Can be harmonic or inharmonic

Overtones

Similar to harmonics but numbered differently

Anything that is higher than the fundamental frequency

1st harmonic = fundamental frequency

2nd harmonic = first overtone

Inharmonicity

Crucial for understanding speech consonants (Fricatives and plosives)

Fourier Analysis

All waves decomposed into sine waves

Fourier Synthesis

Combines sine waves to create complex waves

Line Spectrum

Sharp vertical lines; used for periodic signals (musical notes)

Each peak represents a harmonic

Height indicates the amplitude

Continuous Spectrum

Continuous frequency representation; used for non periodic signals

Spread out energy across frequencies

No distinct harmonies

Spectrogram

Displays how frequencies change over time

Periodic Waves

Repeat at regular intervals and contain harmonics

Aperiodic Waves

Do not repeat and have a broad frequency spectrum

Ex: /s/, /sh/ sounds

White noise

Equal intensity at all frequencies

Appears random and consistent

Used for sound masking, testing equipment, audio calibration

Pink Noise

Equal energy per octave (more energy in lower frequencies)

More balanced to human hearing

Used in audio testing, acoustic measurements, sound masking

Impulse Sound

Sudden sound bursts containing a broad frequency range (very high energy)

Instantaneous and sharp sounds with high intensity; non repeating

Used for acoustics testing, impact noise, sonic testing, etc.