what do i do to make sure the length and mass per unit length of the wire is constant and tension changes?

Question

many musical instruments contain wires which are stretched between two fixed supports. these wires are often made to resonate in their fundamental mode of vibration.

The frequency of the note produced by the wire when it vibrates depends on 1) the length of the wire between 2) the tension in the wire 3) the mass per unit length of the wire
design an experiment to investigate how the resonant frequency of a wire vibrating in its fundamental mode depends on the tension in the wire.
in your account pay particular attention to
a) the method by which the wire would be made to vibrate at a known frequency
b)how the resonant frequency and the tension would be measured
c) the procedure to be followed
d) control of variables
e) safety precautions which you would take.

Answer 1

First, I'm assuming that your question is "what do i do to make sure the length and mass per unit length of the wire is constant AS tension changes?" (note change of 'and' to 'as') and the rest of the material is just for explanation.
The answer is, you can't keep M/L constant. If your setup actually uses two fixed supports, L will be constant, but tensioning the wire stretches it, removing some M from between the supports. You can measure the amount of stretch by making two benchmarks (maybe small pieces of masking tape) in the unstretched wire and measuring their distance as you change the tension. (Doing the appropriate scaling between the baseline distance and the length of the stretched wire.)
For the theory on wire tension and resulting dimension changes, search Poisson's ratio. Basically stretching a length L of wire by epsilon*L (epsilon is a small number) would result in a thinning of radius R of 0.5*epsilon*R if the material were incompressible (thus inexpandable). However all solids including steel expand under tension to some extent, so the Poisson ratio of 0.5 above is more typically 0.25 to 0.35 for metals. See the ref.