   Chapter 13, Problem 58P

Chapter
Section
Textbook Problem

The elastic limit of a piece of steel wire is 2.70 × 109 Pa. What is the maximum speed at which transverse wave pulses can propagate along the wire without exceeding its elastic limit? (The density of steel is 7.86 × 103 kg/m3.)

To determine
The maximum speed of the transverse wave pulse.

Explanation

Given info: The elastic limit of the steel wire is 2.70×109Pa . The density of steel is 7.86×103kgm-3 .

The wave speed in a stretched string is given as,

v=Fμ (I)

• 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 tensile stress can be written as,

S=FA

• S is the stress
• A is the area

Rearrange in terms of F .

F=SA (II)

The linear density of the string can be defined as,

μ=mL (III)

• μ is the linear density of the string
• m is the mass of the string
• L is the length of the string

Substitute (II) and (III) on (I),

v=SA(mL)=SA

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