# Thread: variations (direct, inverse, etc...)

1. ## 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:

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

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?)

2. 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.