# Conducting a fourier series given amplitude and frequency

I'm currently writing an extended essay on why instruments sound different when they play the same notes, I have recorded a few instruments and plan on setting up some data but I have no Idea what data I should be looking at. I know I should be looking at fourier series but after watch videos I see that a fourier series is used to model a sinusoidal wave.

How does this connect to instruments other than the fact that they also produce sinusoidal waves, should I instead be looking at turning the initial sound wave into a frequency-amplitude graph. I understand all the mathematics involved but where do I start?

• This might be a start en.wikipedia.org/wiki/… you know what you want to do better than I, but out of curiosity I wonder how do you account for the different materials, structure, size of instruments?
– user108787
Sep 2, 2016 at 23:07
• I understand all the mathematics involved but where do I start? The frequency/amplitude relationship determines the timbre of a musical note. Start perhaps by comparing square wave and saw tooth wave forms and their frequency/amplitude spectra?
– Gert
Sep 2, 2016 at 23:40
• You need to compare acoustic spectra, ie amplitude v frequency. However, this only confirms that the sound from different musical instruments is different. To understand why they are different you need to examine the modes in which the instruments can vibrate - which is a very difficult topic. Sep 3, 2016 at 22:06