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Finding the relationship between wave speed and tension in a standing wave 
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#1
Feb2310, 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=fλ v = √(t/μ) y = (x1)/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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