Respuesta :
Answer:
v = 64.14 m/s
Explanation:
First we are going to calculate the initial tension force in the wire.
How:
[tex]V = \sqrt{\frac{T}{\mu} }[/tex]
Where v: Wave's speed
T. Tension force
μ: Linear densityof the wire
Then:
[tex]T = V^{2}\mu[/tex]
[tex]T = 46^{2}(7 x 10^{-3}) = 0.322N[/tex]
Now we calculate the linear dilation of the copper, thus
ΔL = αLoΔT
Where α:The coefficient of linear expansion for copper
ΔL = [tex](17x10^{-6})( Lo)(-14) = 0.000238 Lo[/tex]
The Young's modulus is defined like:
[tex]E = \frac{TLo}{A\Delta L}[/tex]
Where E : The Young's modulus
A: cross-sectional area
Then
[tex]T = \frac{EA\Delta L}{Lo}[/tex]
[tex]T = \frac{1.1 x10^{11} (1.1x10^{-6} )(0.000238Lo)}{Lo} =28.798 N[/tex]
and the speed of the wave when the temperature is lowered is:
[tex]v = \sqrt{\frac{28.798}{7x10^{-3} } } = 64.14 m/s[/tex]
