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Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

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BuyFindarrow_forward

Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

Review. The elastic limit of a steel wire is 2.70 × 108 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire without exceeding this stress? (The density of steel is 7.86 × 103 kg/m3.)

To determine

The maximum speed at which transverse wave pulses can propagate along the wire.

Explanation

The elastic limit of a steel wire is 2.70×108Pa and the density of steel is 7.86×103kg/m3.

Formula to calculate the maximum speed of pulses is,

  vmax=Tμ        (I)

Here, vmax is the maximum speed of pulses, T is the tension in the wire and μ is the linear mass density of wire.

Formula to calculate the tension in the wire is,

    T=P×A

Here, T is the tension in the wire, P is the elastic limit of wire and A is the area of the wire.

The relation between the linear mass density and volume mass density is,

  μ=ρA

Here, ρ is the volume mass density.

Substitute P×A for T and ρA for μ in equation (I).

  vmax=P×AρA=Pρ

Substitute 2

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