Finding the relationship between wave speed and tension in a standing wave

[Eutrophicati]

Homework Statement

The problem is the same as the title; to find the relation between wave speed and tension for a standing wave in a string. (Fixed ends)

Given data (from the experiment)

String length = 1.62m, mass is negligible
Frequency = 48.2 Hz
Basically one end of the string was attached to a vibrator with adjustable frequency and the other end suspended across a pulley from where weights could be attached.

These are the recorded results:
Tension :: Number of nodes
0.981 - 4
1.962 - 3
3.924 - 2
7.848 - 1

Homework Equations

v=fλ
v = √(t/μ)

y = (x-1)/2
I used this last one to find the *number of wavelengths* (not the wavelength itself) in the standing wave where x is the number of nodes.

The Attempt at a Solution

I used the number of nodes to calculate the wavelength (length provided as 1.62)
Tension :: wavelength
0.981 - 1.08
1.962 - 1.62
3.924 - 3.24
7.848 - 6.48

And I used
v=fλ, where f = 48.2 to calculate wave speeds. I got 52.06; 78.08; 156.17; 312.34.

I also used v = √(t/μ) to calculate a theoretical speed to plot against the experimental, but I got the same value every time by that method (around 3.967 ms^-1).

Well, at the moment, I just want to know what the relationship between tension and wave speed SHOULD be theoretically. (just an equation)
I'm hopelessly confused right now...

Edit: If I can understand the relation I should be able to plot a graph for my experimental values, hopefully I can make some sense out of the results

Edit 2: I thought of this earlier but I keep loosing track since I have no firm grasp on the concept
v = √(t/μ)
Isn't THIS the relation between wave speed and tension itself? :s

 

[kuruman]

Starting from the last question, yes $v=\sqrt{T/\mu}$ is the correct equation relating the propagation speed to the tension. For a fixed tension, you get a fixed speed. If you vary the frequency, you simultaneously vary the wavelength because the product $\lambda f$ is fixed. Is this an experiment where you fixed the frequency and varied the tension until you got a certain number of nodes? Please describe what you did to get the numbers you posted. Specifically, what did you do to get the pairs of tensions and wavelengths. Also, please remember to attach units to any numbers that have dimensions. This is particularly important in lab experiments.