## Noise

• It is easy to produce sound that contains a jumble of frequencies

• Wind and wave sounds are examples of noise, non-repeating signals characterized by statistical randomness

• Because noise is non-repeating but continuous, it does not have a characteristic frequency / tone; it is accurate to think about it as containing randomly varying components of all audible frequencies

## Impulse

• Gunshots and claps are examples of impulses: a single pressure spike propagates through the air

• The impulse can initially be thought of as containing all audible frequencies

• Impulses will be damped by travel through the air, decaying into silence quite rapidly

## Vibration

• A string or reed, for example, will vibrate in response to an impulse or noise

• Vibration is typically repetitive, with a characteristic frequency f

• Vibration will also typically contain multiples of the fundamental frequency f: 2f 3f 4f etc at lower amplitudes. These are called harmonics, are due to nonlinearity in the vibrating material, and are important to the sound

• Vibration is the classical solution to the ordinary differential equation describing a spring-mass system

$$m \frac{d^2 x}{dt^2} = -k x$$

for some "mass" m and "spring constant" k, namely

$$x = A ~ \textrm{cos} ~ \sqrt{\frac{k}{m}} t$$

where the amplitude A is arbitrary. In practice A is determined by the excitation of the system: an impulse decays, a noise persists

## Resonance

• A resonant cavity is a filter: amplifies frequencies near wavelength (and multiples), suppresses other frequencies. Wikipedia has a nice explanation for various common cavities

• Most sound-producing things operate in/with a resonant cavity: voice, instruments, etc

## Natural Sound — Acoustic Instruments

• Noisemaker + resonant cavity

• Wind: buzzing lips, vibrating reed, tube

• String: vibrating string, usually cavity

• Percussion: impulse, usually cavity

• Misc

• Pitch adjustment by tension or length; cavity length modification via holes (or slide) — so many choices

• Most but not all monophonic: one sound at a time

## Natural Sound — Voice

• The human vocal tract

• Breath exciting vibrating sound source ("vocal chords" — actually vocal folds), resonant cavity (larynx, mouth, etc)

• Frequency range unsurprisingly similar to hearing range