@77jovian You may find the following writeup to be instructive. (Coincidentally, btw, as you had also done it uses the example of a flute for illustrative purposes):
http://newt.phys.unsw.edu.au/jw/sound.spectrum.html Note particularly the figure in the section entitled "Spectra and Harmonics," which depicts the spectrum of a note being played by a flute.
To provide context, a continuous pure sine wave at a single frequency (which is something that cannot be generated by a musical instrument) would appear on this graph as a single very thin vertical line, at a point on the horizontal axis corresponding to the frequency of the sine wave.
The left-most vertical line in the graph (at 400 Hz) represents the "fundamental frequency" of the note being played by the flute. The vertical lines to its right represent the harmonics. The raggedy stuff at lower levels represents the broadband components I referred to earlier. Note this statement in the writeup:
... the spectrum is a continuous, non-zero line, so there is acoustic power at virtually all frequencies. In the case of the flute, this is the breathy or windy sound that is an important part of the characteristic sound of the instrument. In these examples, this broad band component in the spectrum is much weaker than the harmonic components. We shall concentrate below on the harmonic components, but the broad band components are important, too.
Now if a second instrument were playing at the same time, the combined spectrum of the two sounds at a given instant would look like what is shown in the figure for the flute, plus a number of additional vertical lines corresponding to the fundamental and harmonics of the second instrument, with an additional broadband component that is generated by the second instrument summed in. ("Summed" in this case refers to something more complex than simple addition, since timing and phase angles are involved; perhaps "combined" would be a better choice of words). And since when we hear those two instruments in person our hearing mechanisms can interpret that complex spectrum as coming from two different instruments, to the extent that information is captured, preserved, and reproduced accurately in the recording and playback processes our hearing mechanisms will do the same when we hear it in our listening room.
Best regards,
-- Al
