Solving String Tension: Wavelength, Speed and Frequency

[gillyr2]

Homework Statement

string is under tension 400N. A 1m string has mass 5grams. what is the speed if the wavelength is 1m. What is the speed if the wavelength is .5m. What is the frequency?

Homework Equations

v = sqrt(Tension/(m/L))
v = f * wavelength

The Attempt at a Solution

a) v = sqrt(400N / (.005kg/1m) = 283m/s

b) I am confused. whether to use the first or second equation?
v=sqrt(400N/.005kg/.5m) = 200m/s

c) f = v/wl = 200m/.5ms = 400Hz

is this correct?

 

[gillyr2]

just a push in the right direction would be highly appreciated

 

[Snazzy]

L is the entire length of the string. Why would the linear mass density, something that is inherent and doesn't change with the same string, be changing?

 

[gillyr2]

so for b) would it be 1m for both, or is the speed impossible to derive from that formula?

 

[Snazzy]

If $$V=\sqrt{\frac{T}{\mu}}$$

What do you hypothesise if mu and T are always constant?