Answer :
The tension on the aluminum wire is 52.02 N.
The speed of a wave on a string is equal to the square root of the tension divided by the mass per length. The formula used to calculate this speed of a pulse on the rope (the speed of a wave on a string under tension) is given by |v| = √(T/μ) where v is the speed of a wave, T is the tension on the wire, and μ is linear density (μ=m(mass)/L(length)).
Given the density of aluminum (ρ) is 2700 kg/m³, the diameter of the wire is 4.6-mm or 4.6 x 10⁻³ m, and the speed of the wave is 38 m/s.
First, find the area of the aluminum wire,
[tex]A = \frac{\pi d^2}{4}\\A =\frac{ \pi\times (4.6 \times 10^{-3})^2}{4}\\A = \mathrm{1.66 \times 10^{-5}\;m^2}[/tex]
Now, find the linear density of the wire,
[tex]\mu = \rho A\\\mu = \mathrm{2700\;kg/m^3 \times 1.66 \times 10^{-5} m^2}\\\mu = \mathrm{0.045\;kg/m}[/tex]
Substitute the value of linear density in the speed of wave formula to get tension.
[tex]\begin{aligned}34&=\sqrt{\frac{T}{0.045}}\\34^2&=\frac{T}{0.045}\\T&=1,156\times0.045\\&=\mathrm{52.02\;N}\end{aligned}[/tex]
The answer is 52.02 N and option c is correct.
The complete question is -
The density of aluminum is 2,700 kg/m3. If transverse waves propagate at 38 m/s in a 4.6 mm diameter aluminum wire, what is the tension on the wire?
a) 65 N
b) 39 N
c) 52 N
d) 78 N
To know more about the speed of waves:
https://brainly.com/question/15031238
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