I'm trying to put together a little physics project, and I've constructed a rudimentary stringed instrument using a 2-liter bottle and some string. The string is fed through the bottom of the bottle and wound around a small dowel at the top end, and a small hole has been cut near middle of the bottle so you can put a finger inside to pluck the string. I want to determine the tension force on the string, and then find the increase in tension with each full turn of the dowel. I know that the tension can be found from the equation fλ=sqrt(F/u), where f is frequency, F is the tension force and u is the linear density of the string. I've found u by dividing the length of the string by its mass. After winding the string, I use a guitar tuner to find frequencies. My questions are: If I use the equation v=λf to find λ, would v simply be the speed of sound in air? When I wind the string around the dowel, can I even use my original value for u since the string will be stretched? Any suggestions or enlightenment would be much appreciated!