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

by Eutrophicati
Tags: relationship, speed, standing, tension, wave
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Feb23-10, 05:21 PM
P: 10
1. The problem statement, all variables and given/known data
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

2. Relevant equations
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.

3. 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
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