Fundamental frequency and changes to it

[brunettegurl]

Homework Statement

A stretched wire vibrates in its fundamental mode at a frequency of 384 Hz. What would be the fundamental frequency if the wire were half as long, its diameter were doubled, and its tension were increased five-fold?

Homework Equations

F= $$\frac{1}{2L}$$$$\sqrt[]{\frac{T}{\mu}}$$

The Attempt at a Solution

ok i know that this F= $$\frac{1}{2L}$$$$\sqrt[]{\frac{T}{\mu}}$$ is the formula for the one where F1= 384 Hz

i know that length is cut in half and that tension increases by 5and when the diameter is doubled that means mass is quadrupled my problem is that i don't know how to show that wrt $$\mu$$
for the second frequency would my equation look like
F2= $$\frac{1}{2(L/2)}$$$$\sqrt[]{\frac{5*T}{4*\mu}}$$
and then if we cancel off the 2 in the l would it look like F= $$\frac{1}{L}$$$$\sqrt[]{\frac{5*T}{\mu}}$$ *$$\frac{1}{2}$$

 

[LowlyPion]

Looks like you have it then right?

384*√5

 

[brunettegurl]

thanx i wasnt sure if it looked right