Solving Ant's Tightrope Wave Problem

[jamesm113]

A large ant is standing on the middle of a circus tightrope that is stretched with tension T_s. The rope has mass per unit length mu. 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.

My answer of A= g lambda^2/(32T_s) is wrong, and my web based homework system tells me I am off by a multiplicative factor.

I got my answer by finding out how much distance it would take for a particle on the wire to go from y=0 to y=A (lambda/4), then finding the time it would take for the wave to travel that length (lambda/4 * sqrt(u/T_s)). I then plugged that into the kinematics equation y=y_o + v_ot+1/2at^2. This gave me A = 1/2at^2, and plugged in the variables I knew, giving me the answer above.

Please help. Thanks!

 

[Andrew Mason]

A large ant is standing on the middle of a circus tightrope that is stretched with tension T_s. The rope has mass per unit length mu. 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.

My answer of A= g lambda^2/(32T_s) is wrong, and my web based homework system tells me I am off by a multiplicative factor.

I got my answer by finding out how much distance it would take for a particle on the wire to go from y=0 to y=A (lambda/4), then finding the time it would take for the wave to travel that length (lambda/4 * sqrt(u/T_s)). I then plugged that into the kinematics equation y=y_o + v_ot+1/2at^2. This gave me A = 1/2at^2, and plugged in the variables I knew, giving me the answer above.

Please help. Thanks!

What does the question ask you to find?

AM

 

[jamesm113]

What is the minimum wave amplitude A_min 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.

 

[quasar987]

There was a thread about this exact question about a year ago:

https://www.physicsforums.com/showthread.php?t=63237&highlight=Ant+on+a+tightrope

The thread is pretty badly damaged but ehild's posts are enlightning if you can decipher them :) Hope this helps.