Thanks. I agree with all of this. But still wonder in a classic instrument build the reactance of the body make the body vibe in sound. In case of an electric instrument this energy is lost but the reaction of the excited body back to the string still exist. So what I do not know if we want to preserve the reaction of the body against the string or we want to isolate the string to interact with the body using high mass couplings ? I still wonder how to manage this.
What I described above is how the flexing and vibration of the whole frame changes the vibration on the string. Which changes what the pickup "hears" and sends to the amp. That's the sound that you hear from an electric bass, coming from the speakers.
In an acoustic instrument, such as a classical guitar, there's another type of vibration going on, in addition to the overall flexing of the frame. The body of an acoustic guitar is built as a hollow box filled with air. The top of the body is thin and flexible, and is designed to flex up and down. The vibration of the strings pushes up and down on the bridge, which pushes on the top, which makes the top vibrate up and down. That motion of the top pushes on the air in front of the instrument and squeezes the air inside the box, creating sound. Without an amplifier and speakers. That's what an acoustic instrument does.
In an acoustic instrument, the bridge is the part that transfers the vibration of the string to the top, and makes the top vibrate. That's the reaction against the body that you are talking about. In an acoustic guitar, the top is built very carefully with the wood properties, the thicknessing, and the bracing underneath, all to make the top vibrate in a particular way. Which shapes the sound that you hear in the air around the instrument.
But the vibration of the top also plays a part in the vibration of the frame overall, which changes the vibration on the string. Which changes the vibration of the top.......It feeds back on itself, which gets really complicated. That's where you get into vibrations getting out of phase due to damping, odd frequency spikes being created in the background, natural frequency resonances, etc.
Shaping the sound of an acoustic instrument gets really complicated because you have the combination of the two vibration modes going on at the same time, through the same parts. The Frame Vibration is the reaction of the frame to the vibration on the the string. And the Acoustic Vibration is the reaction of the body top to the vibration of the bridge, which comes from the vibration on the string.
On an acoustic instrument, making the bridge/saddle very rigid and low mass will do the most efficient job of coupling the string's vibration to the top. But that usually results in a screaming bright high end. More than you usually want. For example, if you used a stainless steel bridge on an acoustic guitar, you probably wouldn't like the sound.
So, on most acoustic instruments the bridge is made from softer materials, usually wood. This will tend to dampen the transfer of high frequency vibration, while passing most of the lower frequencies through to the top. It doesn't boost the low end, it just trims the high end. That's done to shape the sound, turning down the high end. A softer bridge also trims the high end in the Frame Vibration too, reducing the clarity and sustain of the high end notes...on the strings.
Going back to electric basses, Acoustic Vibration has a smaller side effect, too. When the frame starts vibrating in reaction to the strings' vibration, the bass is shaking in open air. The surfaces are pushing the air around and creating sound that you can hear. When you play an electric bass unplugged, and listen carefully, you can hear some acoustic sound from it. That's the frame vibration, creating a little bit of acoustic sound on the side. It's not exactly the same sound that you'll hear from the strings, through the pickup, amp and speakers. But it will give you an idea of what the bass will sound like plugged in.
How loud an electric bass is when played unplugged is an indication of how much Frame Vibration is going on. And therefore, how much the frame of the bass is changing the sound on the strings. A bass built with a rigid frame will be quiet when you play it unplugged. It's smooth and still in your hands. You'll mainly hear the metallic twang of the strings. And when you plug it in through an amp, the sound will be mostly from the strings, the pickup and any onboard electronics. The frame isn't vibrating much, or playing much of a part in changing the sound. Many electric basses are specifically designed to be like this, and that's what some players want.
But if a bass is fairly loud when played unplugged, and you can feel it vibrating in your hands, that means that the frame is vibrating in reaction to the strings. It was built to do that, and it does change the sound on the strings. Which gets heard by the pickup and sent on to the amp.
That's how we Luthiers play around with the sound of electric basses. There's much more to an electric bass than just pickups and electronic circuits. There's a complicated mechanical side too.