An ant with mass m is standing peacefully on top of a horizontal, stretched rope

Question

An ant with mass m is standing peacefully on top of a horizontal, stretched rope. The rope has mass per unit length mu and is under tension F. Without warning. Throckmorton starts a sinusoidal transverse wave of wavelength lambda propagating along the rope. The motion of the rope is in a vertical plane. What minimum wave amplitude will make the ant become momentarily weightless? Assume that m is so small that the presence of the ant has no effect on the propagation of the wave. Express your answer in terms of the variables m, lambda, F, mu, and appropriate constants.

Explanation / Answer

Velocity of a wave in a string (V) = ( T/m ) ^1/2
T - Tension
m - Mass per length

lambda=2pi/frequency k=omega/velocity v=(F/mu)^1/2

A=[g(^2)]/[4(^2)F], where g is the force of acceleration due to gravity.

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