Standing waves hanging in pulley problem

[a077456]

In the calculation of the theoretical speed vtheo. = √(F_T/μ) (7), the mass associated with the length of the string hanging over the pulley was not taken into account. Suppose that the length of string hanging over the pulley is 20cm and that the hanging mass is 100 grams. What percentage error in the theoretical value of the wave velocity would result from ignoring the hanging string mass in this case?

 

[maimonides]

What is $$\mu$$? (check the dimension).
Why would you expect sound velocity to be dependent on length?