Sound
What we perceive as sound is caused by changes in pressure against our eardrums, primarily by waves traversing through the air (although waves can also permeate through other fluids). A wave is an oscillation (vibration), where the air pressure alternates higher (compression) and lower (rarefaction) than its equilibrium level. The magnitude of the change in pressure is called amplitude. If the waves sustain for a long enough duration, their amplitude is directly proportional to their perceived loudness or volume (although this is also dependent upon frequency).
Most of the sound waves generated by musical instruments are periodic, meaning they repeat the same or very similar patterns of amplitude (waveforms) consistently. Sound can also consist of non-periodic waveforms, such as sustained noise and transients, usually caused before or after sounding notes by incidental collisions or rubbing of fingers and the parts of the instruments outside of how they primarily generate sound (rubbing fingers on a string, strings hitting the frets, picks initially touching the strings before releasing them).
The simplest waveform is a sine wave, a smooth alternating rise and fall of amplitude, with a clear crest (point of maximum positive amplitude/compression) and trough (maximum negative amplitude/rarefaction). The number of times the waveform repeats gives us the frequency, which is related to the pitch of the sound. The length of time that passes between crest to crest or trough to trough of each subsequent cycle is called the wavelength and is inversely proportional to the frequency.
Digital Signal Processing (DSP) and synthesizers are premised around the idea that sine waves of various frequencies can be combined to produce different (non-sinusoidal) waveforms. This concept is expanded upon mostly on the overtones page. However, also keep in mind chords can be formed by mixing non-harmonic overtone frequencies. Usually these still have a somewhat low whole-number ratio. For example, the just intonation ratios for the M3 and P5 intervals are 5:4 and 3:2. This means for every 4 cycles of the root pitch of the chord, there are 5 cycles for the M3 pitch and 6 cycles for the P5. The crests and troughs of each pitch will align differently with the crests and troughs of the other pitches over that 4 cycle span. This means the combined waveforms of each pitch create an entirely new waveform with a larger wavelength. We can hear how a chord sounds unique compared to its individual notes, although we rarely bother trying to determine the frequency of its unique waveform, since it is not clearly related to pitch like a standalone sine wave.
The interaction of multiple waves creates interference patterns. When waves both have positive or negative amplitude simultaneously, this creates positive interference, summing their combined amplitudes making the pressure difference from equilibrium even stronger. When waves have different positive and negative amplitudes simultaneously, this creates negative interference, reducing each other's amplitude.
Phase describes the "starting position" of a wave, described in terms of degrees (0 - 360). When two waves have the same frequency and phase, their crests and troughs align, creating complete positive interference. The combined wave looks identical to the original, only with a larger amplitude. When two waves with identical frequency have complete opposite (180 degree difference) phases, the crests align with the troughs, resulting in complete negative interference. The combined wave is not a wave at all, but a constant equilibrium pressure level - the waves cancel each other out.
Whenever combining multiple audio sources, particularly two or more microphones for the same instrument, signals may arrive delayed, causing different interference patterns throughout various frequencies. This is known as a comb filter (sometimes also called being out of phase), with frequency nulls occurring routinely throughout the audible frequency spectrum.