The density of aluminum is 2700 kg/m³. If transverse waves travel at $38 \mathrm {~m} / \mathrm { s }$ in an aluminum wire of diameter $4.6 \mathrm {~mm} \text {, }$ what is the tension on the wire?

Question

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The correct answer is A.The tension on the wire is given by:$$T = \mu v^2$$where:* $T$ is the tension in newtons* $\mu$ is the linear density of the wire in kilograms per meter* $v$ is the wave speed in meters per secondThe linear density of the wire is given by:$$\mu = \rho A$$where:* $\rho$ is the density of the wire in kilograms per cubic meter* $A$ is the cross-sectional area of the wire in square metersThe cross-sectional area of the wire is given by:$$A = \frac{\pi d^2}{4}$$where:* $d$ is the diameter of the wire in metersSubstituting these equations into the equation for tension, we get:$$T = \rho \frac{\pi d^2}{4} v^2$$Plugging in the given values, we get:$$T = (2700 \mathrm{~kg/m^3}) \frac{\pi (4.6 \times 10^{-3} \mathrm{~m})^2}{4} (38 \mathrm{~m/s})^2 = 65 \mathrm{~N}$$

The Density of Aluminum Is 2700 Kg/m3 38 m/s38 \mathrm {~m} / \mathrm { s }38 m/s

The Density of Aluminum Is 2700 Kg/m³ $38 \mathrm {~m} / \mathrm { s }$