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Ant Joy Ride. You place your pet ant Klyde (mass m) on top

Chapter 15, Problem 55P

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QUESTION:

Ant Joy Ride. 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 A and amplitudes 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. (a) What is Kiyde’s top speed as he oscillates up and down? (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, and by what factor?

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QUESTION:

Ant Joy Ride. 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 A and amplitudes 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. (a) What is Kiyde’s top speed as he oscillates up and down? (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, and by what factor?

ANSWER:

Solution 55P Step 1 of 4: Given data, 3 3 Density of steel, =7.8× 10 kg/m Tension or force, F= 900 N Mass of the string made of steel, m=4 g 3 3 Using 1g =10 kg m=4× 10 kg Breaking Stress of the steel, s=7× 10 N/m 2 To find, Radius of the string, r= Length of the string, L= Highest fundamental frequency in string, f=

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