Like for example when I’m listening to an orchestra I can hear a clarinet and a violin quite distinctly from one another, but they’re both sounds vibrating through the same air. Logically, shouldn’t one air only be able to carry one frequency (Vibrate in only one way)? How does the air contain so many frequencies simultaneously?
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The one item missing here is to understand that what we perceive as “time” when it comes to sound is not how we typically think of time. When we normally think of “now”, it’s an instantaneous moment, like a single frame of a movie when you hit the pause button. At that instant, the air a sound wave (or multiple waves) is moving through has a discrete pressure at any particular location (but may be different at different locations). In the case of multiple waves, the pressure at any location reflects the sum of all the waves passing through that spot. Pressure, however, doesn’t generate sound. Sound is generated by changes in pressure, which requires some amount of time to let the waves move through. Hence the sound you here right ‘now’ is actually your brain sampling over several ‘nows’. The more time points your brain samples over, the more accurately it can make judgements about pitch (the reverse is also true). Hence a sound wave played for only a tiny fraction of a second is too short for your brain to figure out a pitch, and instead it sounds like a ‘bang’ of a drum. Play the same sound for longer and it begins to actually have a tone (or multiple tones). You needed the extra time to figure out what the sound was, but you didn’t even realize you were doing it.
So this brings us to the last part: how does a sound contain multiple sounds in it? if each single sound is a wave of a single frequency, then a combined sound is a wave of multiple frequencies. The combined sound wave excites all the neurons that detect the component frequencies over the same period of time that you heard the combined wave, and each frequency has an intensity (volume) of detection corresponding to how loud each component in the wave was.
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