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

Question

Quizplus · Accepted Answer

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:$$A = \pi r^2$$where:* r is the radius of the wire in metersSubstituting these equations into the equation for tension, we get:$$T = \rho \pi r^2 v^2$$Plugging in the given values, we get:$$T = (2700 \mathrm{~kg/m^3}) \pi (0.0023 \mathrm{~m})^2 (38 \mathrm{~m/s})^2 = 65 \mathrm{~N}$$

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 $38 \mathrm {~m} / \mathrm { s }$