How does a wave carry all of the complexities of sound?

Strictly speaking, most sound aside from that coming from musical instruments or other highly resonant sources is not sinusoidal in nature, and even then most musical instruments will modify the tone characteristics such that they do not play a pure musical tone. A complicated collection of sine waves may be used to approximate most transient sounds over a finite interval with with randomly distributed sources something like white noise the collection will be constantly varying instead of being of being a unique set of tones.

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