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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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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