Curious about Linear Density (μ) of a string

[erinec]

(Sorry I cannot follow the question format because this question is related to a problem, but is not the problem itself.)

I am talking about the linear density μ that appears in this equation:
v = sqrt(T/μ)

.. used usually for musical instruments, where μ = m/L

Now, I am wondering which value of L we use.

Say that you have a string that is normally .1 kg and .10 meters long.
Now let's say that u stretch the string to .12 meters to make some musical instrument.

For L value, do we plug in .12 meters or .10 meters?

Thanks!

 

[rl.bhat]

Usually in the musical instruments that mush stretching is not allowed. mu is the linear density of the wire. For a given length of wire ( which is usual in all the string instruments) linear density depends on the diameter and the material of the wire.

 

[erinec]

But I specifically came across a question that required me to make a choice between using an unstretched length vs. a stretched length and I wasn't sure what to do.Let's hypothetically assume that someone stretched a .1 m wire to .12 m to create some musical instrument.
Which value of L would u use?

 

[rl.bhat]

Obviously 0.12 m.