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

$\displaystyle

Velocity = \sqrt {\frac{Tension}{mass/length}}

$

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

$\displaystyle

Mass \propto \frac{Tension*Length}{Velocity^2}

$

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?)