Music can be described as "the science or art of ordering tones or sounds in succession, in combination, and in temporal relationships to produce a composition having unity and continuity". Since the sounds we make with guitars are usually in the pursuit of music, I think we should begin here.
The word "sound" has many uses and meanings. For one last grasp at science before we leave the station, we'll use this definition: "mechanical radiant energy that is transmitted by longitudinal pressure waves in a material medium [as air] and is the objective cause of hearing".
As we get closer to "the secret of sound" and how a guitar makes it, you may find that it is best to simply hold onto the Greek mousike - any art presided over by the Muses - or the Sanskrit svanati - it sounds.
While the definitions for sound and music can be clearly defined and there have been many experiments with guitars and scientific measurements published, I don't belive that a guitar can be properly defined or described with words. Only a guitar can define a guitar.
What I would like to do here is describe, in my own words, how a guitar produces sound. It is one of the basic building blocks and should be well considered when designing the greatest of musical instruments.
First, a sound starts in your brain...or in that piece of music that came from someone else's brain..or your heart or soul..or whomever is running your body at the moment....So..you choose a note and its character...you press the string tightly behind a fret while your thumb presses the back of the neck and reach down with your finger, thumb or pick and lay into the string - wait!
Before you let go of the string or pull the pick past it, take note of what has happened. No sound has been made and the whole guitar has changed shape. Try this at home: Pluck the A string and pull on the big E string. It works like a tremolo bar. Pull on the E string and the A string lowers in pitch. Any acoustic guitar will do this. As you pull the string sideways, the top of the saddle moves forward, the top behind the bridge rises, pulling the top of the tailblock towards the neck. the top in front of the bridge lowers and depending on whether the top there is convex, flat or concave, the sides may be pulled inward or pushed outward. The neck also moves. The entire guitar is storing energy created when you pressed the pick onto the string. Now let go.
The guitar quickly returns to its at rest shape and overshoots as the string returns to its at rest shape, overshoots and begins to vibrate in an elliptical pattern. Even if you plucked the note perfectly, all the wiggling the guitar is doing will throw it around until it does the same thing orbiting planets do for all the same reasons. The point in time between when the centering force -string tension and guitars resilience- is upset and the string starts vibrating smoothly can be described as the "attack" portion of the note.
Now the string is vibrating -it looks flat and it's close but trust me, it's an ellipse. You need to understand this in order to understand what happens next. Pluck sideways on a string and then down. Hear the difference? No? You need a better guitar.
So, the string is vibrating and the bridge is rocking back and forth like a see-saw. It is also rocking side to side like a see-saw and setting up alternating vibrations all over the guitar. A multitude of ripples traveling across the top, up and down and across the braces, to the back, the sides, the neck...also, at the point where the string meets the saddle, the mass of the string drives the bridge in a direction perpendicular to the string thus adding complexity to an already complex event. The point where the string meets the saddle is vibrating in an egg shape. It could be a cigar shape or a perfect ellipsoid or even a sphere but it is definitely a three dimensional shape.
As the guitar starts vibrating something else happens. Up until this point I have only been referring to the reaction as the guitar is driven by the motion of the string. All the materials in the guitar have their own resonance. This is determined by mass, density, stiffness, and shape. The shape is determined by the luthier and the other qualities can be affected by curing or age but only slightly. These qualities and the resulting combined resonance of all the parts in a guitar work to either help or hinder the production of sound. What usually happens is; Different parts of the guitar resonate at different frequencies and, hopefully, everything dovetails to make a nice even sounding guitar.
This is the part of guitar design that has been highly emphasized and most often scientifically measured. Choosing and shaping the parts of a guitar to arrange the resonant qualities is important. The need for a guitar to be easily driven by the strings is just as important, maybe more so.
Which brings us to the big fat monkey in the middle of the room. Air. All the vibrations in the guitar could go on and on and you wouldn't hear them without air. The principal medium necessary for the transmittal of sound can cause problems in the guitar or be used in your favor.
The primary resonance of any acoustic guitar is usually the "Heimholtz resonance". It can be demonstrated by blowing across the top of a pop bottle, drinking a little, and then doing it again. The tone it makes is determined by the volume of air inside the container and the area and length of the opening. When a guitar vibrates at this frequency, all of its vibrations are nearly cancelled as the whole guitar tries to breath in and out through its sound hole. The note is killed by the resistance from moving all that air.
On a guitar, you can change this resonance by changing the size of the sound hole but you have to change it by about 50% to get a one note difference. A guitar would look pretty stupid with a 2" or 6" soundhole. The first M1's had really light bracing. I reduced the sound hole diameter by a tenth of an inch to keep the top from washing out through hard playing. It's kind of like a little compressor. In its most drastic form it is one of those rubber plugs used for amplified guitars on stage. This is the only reason for changing the size of the sound hole.
Changing the position of the soundhole can make a difference. This is one of the reasons violins and some guitars have sound holes in different positions. With a traditional guitar you are stuck with the sound hole in the middle and have to make the best of it.
The Reynolds number is another factor. This is a measurement of how far air will travel over a surface before it separates from the surface and becomes turbulent. How the sound bounces off some parts and sticks to others inside a guitar makes a difference in how it sounds.
This is all just about one note. What happens when you play a couple notes over the top of each other? A chord picked or strummed? Harmonics where a string vibrates at different directions at the nut and bridge?
A good builder is faced with all these elements of guitar behavior when choosing materials for a new guitar. The desired character of sound and specific wood requests must also be considered. I believe the intuitive method is best used for designing guitars. Instead of choosing flavors and colors like you are in an ice cream parlor, just open your mind and see what pops in there. You will probably be much closer to having something that looks, plays, and sounds as if it popped out of the sky from God.
