You may be thinking more about the difference between a surface finish like polyurethane or oil varnish versus a penetrating oil finish, rather than synthetic vs. natural. Varnish is a lot like paint (but clear, of course) in that it forms a protective layer that sits on top of the wood. Penetrating oils (like the typical Minwax finishes; VelvitOil is terrific, if you can find it at a wooworking store) carry resins into the pores of the wood and harden the tissues of the surface layer of wood, rather than forming a coat over the wood. So, wood finished with a penetrating oil finish leaves more texture to the wood.
Both varnishes and penetrating oil finishes can come in either natural or synthetic forms. For example, Tung Oil is a natural penetrating oil finish, and Minwax and VelvitOil are penetrating oil finishes made with synthetic resins.
All of these differences in finishes may have an effect on reflectivity, absorption, diffusion, and the flexibility of the surface they are applied to. I would think you could hear these differences if they were big enough, but I can't give you any empirical advice.