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Math Help - variations (direct, inverse, etc...)

  1. #1
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    variations (direct, inverse, etc...)

    My class and I are learning about waves. We did an experiment and the equation for the velocity of a transverse wave was given:

     <br />
Velocity = \sqrt {\frac{Tension}{mass/length}}<br />

    I rearranged the equation to try to find the relationship between velocity and mass and I ended up with:

     <br />
Mass \propto \frac{Tension*Length}{Velocity^2}<br />

    But I could not make sense of the relationship between Velocity and Mass. (that square threw me off whether it was left there or if I had completely simplified the problem) What is the relationship between velocity and mass?

    Does it mean that if the mass goes up by a factor of 2, velocity goes up by the factor of 4? (So if I were to increase the mass of the spring, I would increase the velocity of the wave by a factor of 4?)
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  2. #2
    MHF Contributor
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    You almost have it. Why do you doubt?

    You have two problems.

    1) You are backwards. 2x velocity results in 4x mass, not the other way around.

    2) Also, velocity-squared is in the denominator, so a 2x increase in velocity will result in a 4x DECREASE in mass.

    Why don't you try a few values and see for yourself. No problem with a little exploration.
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