Wood tends to leach out tannic acids, and any acid tends to lower pH, depending on how strong, and concentration of the acids. This however depends on the natural buffering capacity of your tap water.
If a piece of woods old, it has probably already leached much of the acids out, the more newly cut from the tree, the more tannins acid will be released.
If you have Amazonian fish, tannins are desirable, because those tannic acids have an anti-bacterial component, and produce various stages of tea stained (black (Rio Negro type)) water.
The same way the tannins in green tea work.