Can somebody please provide a thorough and neat explanation to the question? I w

Question

Can somebody please provide a thorough and neat explanation to the question? I would just like to understand the concept behind it so please explain the purpose of each step. Thank you!

An aluminum wire is clamped at each end under zero tension at room temperature (22° C). The tension in the wire is increased by reducing the temperature, which results in a decrease in the wire's equilibrium length. What strain (AL/L) will result in a transverse wave speed of 100 m/s? Take the cross-sectional area of the wire to be 5.0 × 10-6 m2 Furthermore, you should use the following properties of aluminum: density, ? 2.7 × i03 kg/1n3, and Youngs modulus, Y : 6.8 × 1010 N/m2. Assume two significant digits.

Explanation / Answer

wave speed=sqrt(Tension/mass per unit length)

let length of the wire be L.

mass per unit length=density*cross sectional area

=2.7*10^3*5*10^(-6)=0.0135 kg/m

as speed given is 100 m/s,

100=sqrt(tension/0.0135)

==>tension=135 N

as force=young's modulus *cross sectional area*strain

==>strain=135/(6.8*10^10*5*10^(-6))

=3.97*10^(-4)

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