An ant with mass m is standing peacefully on top of a horizo

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, Cousin 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.

Solution

As we know, wave velocity, v = square root(Tension/mass per unit)

= root(F/u)

Now, Frequency of oscillation of ant, n = velocity/wavelength = v / lemda = (1/lemda)*root(F/u)

max acceleration = square of (2.PI.n) * Amplitude

for ant to feel weightless, acceleration has magnitude = acceleration due to gravity = g

=> g = (2.PI.n)^2 * Amplitude

=> Amplitude = g / (2.PI.n)^2, where n = (1/lemda)*root(F/u)