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Homework Help: Gradient of Wavelength vs Period Graph?

  1. Sep 10, 2010 #1
    We've got a table of periods (in seconds) and their corresponding wavelengths for creating resonance in a closed pipe.

    I've been told that plotting a graph of period (on x axis) vs wavelength, and finding the gradient of that linear line will tell me the speed of sound in air. I can do that easily and found the speed in air to be 375m/s - which is reasonable.

    I want to know why this works though. Why do I plot a graph of wavelength against period? Why is the gradient the speed of sound in air?

    I'm assuming it is something to do with the linear equation (y=mx + c) relating the the universal wave equation (v = f x lambda). And f being inversely proportional to the period (T). But i have no idea how they relate!

    An in-depth explanation would be amazing! I can do the question easily, I always just want to know why what we've been told to do works :)
     
  2. jcsd
  3. Sep 10, 2010 #2

    rl.bhat

    User Avatar
    Homework Helper

    Your assumption is correct. You know that

    v = f*λ. So

    λ = v/f. Bur 1/f = T. So

    λ = v*T => y = mx.

    The slope of the graph is the velocity.
     
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