Violin strings are either single core materials or of the wound variety with a single core of one material wound with a helix of another (usually heavier) material to give the string a lower resonant frequency. In analyzing the acoustic impedance of a wound string, which part will determine the acoustic impedance of the string , the core or the outside helix material? Or will the overall impedance be somewhere in between the two?
I'm not sure you understand what "acoustic impedance" is. The string by itself has a resonant frequency defined by its elastic modulus, the applied longitudinal tension, and length. If you really want to know how well it couples to the air around it, I suspect you'll be diving into an ugly bit of math. For one thing, unlike a speaker cone or a trumpet (for two examples), the string is coupled to the air along its full length, and primarily in two directions (the plane of vibration).