Re: Knowing the geometry changes of a string, how to calculate new tension?

to know the tension in the string, you have to know the linear strain in
the string. small linear strains are defined as the ratio of the change in
length to the original length. so you could probably mark a 1" on the
string. tighten it just a little bit and find out the new length ( you
would have to use a vernier calliper). then find the difference and divide
it by the original length, which is 1" ( means the difference is the
strain).

now, the linear strain is related to the stress by the material property
called young's modulus, which you would have to know. this relationship is
called hooke's law. basically

stress= strain* Y

then,

tension T= A * stress, A is the cross sectional area of the string.

you have to be careful here. by stretching the string, you make it thinner.
so you would have to calculate the new diameter. you can easily measure
this using  a screw gauge, otherwise use poisson's ratio to calculate the
lateral strain and therefore the new dia.