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

  1. 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 = (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
     
    Last edited: Feb 23, 2010
  2. jcsd
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