   Chapter 13, Problem 50P

Chapter
Section
Textbook Problem

Workers attach a 25.0-kg mass to one end of a 20.0-in long cable and secure the other end to the top of a stationary crane, suspending the mass in midair. If the cable has a mass of 12.0 kg, determine the speed of transverse waves at (a) the middle and (b) the bottom end of the cable. (Hint: Don’t neglect the cable’s mass. Because of it, the tension increases from a minimum value at the bottom of the cable to a maximum value at the top.)

(a)

To determine
The speed of the wave at the middle of the cable.

Explanation

Given info: The mass of the object attached to the cable is 25.0kg . The length of the cable is 20.0m . The mass of the cable is 12.0kg .

The wave speed in a stretched string is given as,

v=Fμ (1)

• v is the wave speed
• F is the tension in the string
• μ is the mass of the string per unit length or the linear density of the string

The linear density of the cable will be,

μ=mcableLcable

• mcable is the mass of the cable
• Lcable is the length of the cable

Substituting mcable=12.0kg , Lcable=20.0m

μ=12.0kg20.0m=0.600kgm-1

At the midpoint, the mass underlying will be the sum of whole mass of the object and half of the cable mass.

munder=25

(b)

To determine
The speed of the wave at the bottom of the cable.

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