Answered

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The density of aluminum is 2700 kg/m3. If transverse waves propagate at 34 m/s in a 4.6-mm diameter aluminum wire, what is the tension on the wire

Sagot :

Answer:

52N

Explanation:

v=SQRT(T/μ), μ=pA, A=πr^2

v=SQRT(T/pπr^2)

v^2=T/pπr^2

v^2*pπr^2=T

34^2*2700*π*0.0023^2=T

T=52N

onyebuchinnaji

The tension on the aluminum wire at the given density is 52.02 N.

Tension in the wire

The tension in the wire is calculated using the following formulas;

[tex]v = \sqrt{\frac{T}{\mu} }[/tex]

where;

  • v is speed of the sound wave
  • T is the tension in the wire
  • μ is mass per unit length

Area of the aluminum wire

A = πd²/4

A = π x (4.6 x 10⁻³)²/4

A = 1.66 x 10⁻⁵ m²

Mass per unit length of the wire

μ = ρA

μ = 2700 kg/m³ x 1.66 x 10⁻⁵ m²

μ = 0.045 kg/m

Tension on the wire

[tex]34 = \sqrt{\frac{T}{0.045} } \\\\34^2 = \frac{T}{0.045}\\\\T = (34^2)(0.045)\\\\T = 52.02 \ N[/tex]

Thus, the tension on the aluminum wire at the given density is 52.02 N.

Learn more about tension on wire here: https://brainly.com/question/14336853

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