When it comes to acoustic guitars, the tone comes from the pick, strings, then the guitar body, the room tone, and then finally the mic placement. And there are countless factors between these elements--for example, the bracing style inside the guitar body has a massive effect on how the body resonates. The types of wood the body, top, and fretboard determine which frequencies are absorbed more than others when reflecting sound waves. The thickness, texture, and shape of the pick really matters, too, not to mention the placement and angle of the pick as well. All these elements color the guitar's tone in different ways.
Something as minuscule as the thickness of the guitar pick can really change a lot. Let me give you some examples to listen to, so this makes sense.
Here are some samples of various pick thicknesses, played on a Martin D16:
0.50 mm pick test
0.60 mm pick test
0.73 mm pick test
0.80 mm pick test
1.14 mm pick test
You'll notice that the thicker the pick used, the more emphasis on the mid frequencies, giving the guitar a warmer and deeper tone. Thin picks sound bright and delicate, emphasizing the high frequencies--of course, this is an oversimplification in terminology, since what's happening is certain formants are being amplified more than others. The main point is to distinguish these two polar opposites in tone according to pick thickness. That's why a popular favorite is the 0.73 mm pick, since it gives you a well-balanced tone.
Essentially how the string vibrates is a result of the guitar pick. It then interacts with the guitar body itself, both the exterior (like how the bridge/fret ends of the string mute the string vibration and the actual audio reflection that occurs on the fretboard/top) and the interior. The interior of the body resonates and amplifies the sound, coloring it in its own way.
Naturally, articles can be written solely about how the strings change the guitar's tone, the body wood type, and all the other factors mentioned above. But the undeniable source of the sound--the element which excites the string itself--is the foundation of tone, whether it's a pick, e-bow, finger, or power drill (if you're Van Halen).
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