Eli5:When one speaker is playing two (or more) frequencies of sound, think harmony in music) the resulting sine wave is an average of those two frequencies. How does the brain interpret it as two different notes when one speaker is playing the average of two frequencies?
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>resulting sine wave is an average of those two frequencies.
This is incorrect. The resulting sine wave is a sum of both waves and will retain frequency information of both waves. As the other reply describes, the frequency information is picked up by your ear and then your brain.
One of the key concepts is that waves do not “average”. If you have two sine waves of wavelength x and 0.5x, they do not average to a sine wave of 0.75x. Rather, it forms a complex wave that has wavelength x, but not perfectly sinusoidal anymore. This is hard to describe with words, so feel free to plot this and visualize this (https://www.mathopenref.com/graphfunctions.html).
f(x) = sin(x) for your first sine wave
g(x) = sin(2*x) or any other integer for a different frequency
h(x) = sin(2*x)+sin(x) to simulate the “harmony” or the two frequencies together.
You’d see how the resulting wave shows elements from both waves, but are not an average in any sense when it comes to wavelength/frequency information, only with amplitude.
Fun fact: whether two notes are harmonic or dissonant have to do with whether they have common factors. For example, C and G harmonize because their frequencies are in 2:3 ratio.
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