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I am trying to understand some basics of the acoustic theory.
Can someone in their own simple words explain what are the differences between the waves on two different instruments playing the same note? Such as how does a wave from a G on a guitar differ from a G in the same octave/frequency on a piano?
Also what does the 'bass' effect increase or decrease do to any wave signal you give it?
So, the fundamental difficulty to understand here is that each individual sound is made up of many many composite frequencies. When you play A440 on a guitar, it sounds different from A440 on a piano because the piano has vastly different upper frequency content. You said "the waves", but this is a little bit misleading: The waveform you see when you record guitar or piano is actually the sum of many many frequencies. The only way they are "the same" is that they have the same fundamental frequency -- that is, the lowest audible frequency of these two notes is the same, that is, 440 Hz.
As for how filtering a sound affects its content:
If you put a bass-cut on a sound, you're essentially lowering the volume of the low frequencies of the sound. If you put a bass boost, you're raising the volume.
Key to this is the harmonics of the note. If you just play a 440Hz perfect sine wave it doesn't sound very exciting at all, but add in some of the harmonics and it starts to come alive.
If you add in the waveforms at 3x and 5x the fundamental, or at 2x the fundamental you will get a very different tonal effect. Varying the relative amplitude of these also alters the tone. Adding in frequencies which are not a multiple can lead to more atonality (think bells or cymbals)
If you translate the waveform into the frequency domain (ie look at the output of a frequency analyser which has your sounds fed into it) you can see how much these harmonics shape the sounds we hear.
Bass and Treble (or wah and other filters) just boost or cut a particular range of frequencies.
have a look at this wikipedia article for a great starting point, and also search for fourier transform to understand how the time and frequency domains are equivalent.
If you want some quick visualizations.. I suggest you look at the Freesound Project. Especially the tag 'notes'.. You can see how different notes look like and play them to see how they sound..
