How do complex waves and harmonics work?
So from what I understand, a sine wave is a sound wave that vibrates at only one frequency. So a sine wave of 220hz vibrates at just 220 cycles per second. Simple enough. But then on this video I was watching, they started talking about how instruments would sound the same if they played the same note in sine waves and that it's complex waves that make them sound different and give them their timbre. But then in that same video, they said that complex waves are broken into two parts, the fundamental frequency and the harmonics. They said the fundamental frequency is the lowest frequency that we associate with the pitch that an instrument is playing, and all the harmonics are just doubles of the fundamental frequency. So wouldn't that make all instruments sound the same? For example, if you have a cello and trombone both playing at 220hz (fundamental frequency), the harmonics would be the same for both: 440, 660, 880, etc... and I also don't understand how something can vibrate at multiple different frequencies. So something at 220hz with the harmonics 440hz, 660hz, and 880hz vibrate at 220, 440, 660, and 880 cycles per second at the same time? How is that possible?
And to add further confusion. They showed a 3D model of the wave a cello makes and the wave a trombone makes. They said that the fundamental frequency (which, in this case, was supposedly 220hz) is supposed to be the lowest frequency and have the highest amplitude. That's supposedly how our brains are able to hear a certain pitch even though there's multiple pitches at once. But on the model of the cello wave, there were clearly spikes around the frequency range lower than 220hz and then for the trombone wave, although 220hz was the lowest, it didn't have the highest amplitude. If you look up "cello and trombone complex wave 3D model" on Google images, you'll see what I'm talking about. I would post the picture here but it won't let me.
So can someone with more knowledge in this please explain to me how all this works?
