The ability to recast a complex sound as the sum of mulitple sine waves at different frequencies is unintuitive to me, apparently well proven, and old as dirt: French mathematician and physicist Baron Jean Baptiste Joseph Fourier (1768-1830) realized that any complex waveform could be decomposed into a group of sinusoids of different frequencies and amplitudes. Okay, maybe dirt is older than 280 years, but still . . .
So when I strike an open E on my guitar, with a fundamental frequency of about 80 Hz, the string and guitar conspire to establish the harmonics that will be heard as part of te tone. The idea that you can describe that sound as a series of sine waves seems quite intuitive to me. Different acoustic guitars will accentuate different frequencies, so the harmonic content of that open E differs from guitar to guitar. It also differs depending on whether you strike it harder (harmonics become relatively a greater part of the sound) or if you strike the string near the bridge (excites the fundamental less, again resulting in more accentuation of harmonics (twangy sound). That all makes sense to me, and I can see how even if I play a six tone chord, the sound could be defined by the fundamentals and harmonics of each of the notes of the chord.
But it turns out that you can also describe the sound of a bass drum and snare being struck at the same time as a guitar chord, bass guitar note, piano chord and four part horn section as a series of sine waves. Or the sound of a real or made for movies explosion. Really.