an A4 musical note is 440hz in standard tuning. A soundwave of 440hz in air has a wavelength of over 80 centimeters, so how can a speaker cone that moves less than a centimeter back and forth produce that wave? What am I missing about wavelengths of sound?
The key is that the speaker cone does not need to move back and forth the full distance of a soundwave's wavelength in order to produce it. The speaker's movement creates pressure changes in the air around it, which causes those pressure changes to propagate away from the speaker as a soundwave. As long as the frequency of those pressure changes matches that of the desired soundwave, then it will produce it regardless of how small or large its movements are.