Natural Sound
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
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