The input from the bower is very complex but consists of a series of partial resonances. These same resonances appear in the output of the instrument. But the instrument changes them to a great degree resulting in a very distinctive sound to each bass. Everything effects this, from the wood damping to the thickness/graduation of the plates, the stiffness of the sides, the size of the ff holes, the volume of the box.
(If you are still interested, read on, i'm getting to the soundpost)
The force exerted by the bowed strings causes the bridge to rock about the position of the post, causing the other side of the plate (east to west) to vibrate with a larger amplitude. This increases the radiating volume of the instrument and results in a louder sound. It also changes the way the body modes of the instrument vibrate, and effects frequency response of the bass.
This is the physics of it, and you can't change it!
In practice small differences in arching, plate thickness and mass of the individual plates can result in big changes in the resonant frequencies of the bass. Any little change has the potential to effect the response of a particular bass, from a round end post, to a thinner post, to a change in post material. That is why the post can be tapped a little and that will pop a brighter resonance. If you had the ability to measure the response curve quickly and accurately it would be obvious by an increase in amplitude of one (or more) peaks. Tap it the other way and a partial resonance goes down. That is physics and it can't be changed.
Knowing how to effect the change is the HARD part and is why luthiers exist. It is obviously easier to understand this than to be able to tune a bass!!!! It is like tuning an engine by feel. Also just because a change effects the bass in a desirable way to the owner, does not mean it is good for its longterm health.
(now to Traeger)
" Here's a real shocker. Contrary to popular belief the soundpost does not transmit the vibrations of the top to the back", Traeger writes. And " Because the top and back do not vibrate exactly the same way at the same time, they exert a twisting motion on the sound post. The more you can make the soundpost less resistive to this twisting motion, the better the instrument will sound."
Here is that pesky "Better' prase. But the physics are correct.
Thinner post will resist less, as will one with rounded ends. So will an hourglas shaped post. Writes Traeger. Makes sense.
Plywood plates have a higher impedance (resists bending) according to Traeger. And he states that the higher impedance plates need a stiffer wood to match. This is unclear to me.