# Tension and wave motion

1. Oct 29, 2008

### beanieb

1. The problem statement, all variables and given/known data

A large ant is standing on the middle of a circus tightrope that is stretched with tension T. The rope has mass per unit length mu (no symbl). Wanting to shake the ant off the rope, a tightrope walker moves her foot up and down near the end of the tightrope, generating a sinusoidal transverse wave of wavelength lambda and amplitude A . Assume that the magnitude of the acceleration due to gravity is g. What is the minimum wave amplitude such that the ant will become momentarily weightless at some point as the wave passes underneath it? Assume that the mass of the ant is too small to have any effect on the wave propagation.
Express the minimum wave amplitude in terms of T, mu, lambda, g and .

2. Relevant equations

I am assuming the wave is moving with y(x,t)=Asin(wt-kx)

3. The attempt at a solution
I knowthe ant will become weightless when the normal force between the string and the ant becomes zero. This means that I have to find when the maximum accel = -g. So if i differentiate the wave twice to get accel and let this equal to -g i get (unless im wrong)
-Aw2(Sin wt)= -g. Dont know how im supposed to relate this back to tension and mass per unit length or even if im doing this right. Please help

2. Oct 29, 2008

### beanieb

also just thought v=sqrt(T/mu). is Amax = 4(pi)^2 *v^2*?

3. Oct 29, 2008

### beanieb

w^2= 4(pi)^2*(T/mu)

subbing into -g=-Aw^2 Sin wt and rearranging gives:

(4(pi)^2*T)/mu*A=g*Sin (wt)

How do i relater sin(wt) back into the variables I have?

4. Oct 29, 2008

### beanieb

relate sine wt back to lambda? sorry im posting so muchh im working this out as i go