You place your pet ant Klyde (mass m ) on top of a horizontal, stretched rope, w

Question

You place your pet ant Klyde (mass m) on top of a horizontal, stretched rope, where he holds on tightly. The rope has mass M and length L and is under tension F. You start a sinusoidal transverse wave of wavelength ? and amplitude A propagating along the rope. The motion of the rope is in a vertical plane. Klyde's mass is so small that his presence has no effect on the propagation of the wave.

Part A

What is Klyde's top speed as he oscillates up and down?

Express your answer in terms of the given quantities.

Part B

Klyde enjoys the ride and begs for more. You decide to double his top speed by changing the tension while keeping the wavelength and amplitude the same. Should the tension be increased or decreased?

Klyde enjoys the ride and begs for more. You decide to double his top speed by changing the tension while keeping the wavelength and amplitude the same. Should the tension be increased or decreased?

Part C

By what factor should the tension be changed?

Express your answer using one significant figure.

Please show ALL your work so I can understand. Thank you!

Explanation / Answer

so max speed = A w

so v = sqrt(T/(M/L))

and v = lambda f

and w = 2 pi f

sqrt( T L/M) = lambda w/(2 * pi)

w = 2*pi/lambda sqrt(F L/M)

so v max = 2* pi*A/lambda sqrt(F L/M)

b) increased

c) by a factor of 4 since sqrt(4) = 2

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