What is the wave speed in a brass wire

[Batman354]

Homework Statement

What is the wave speed in a brass wire with a radius of 4.65×10-4 m stretched with a tension of 128 N? The density of brass is 8.60×103 kg/m^3.

Homework Equations

v=square root of T/u

The Attempt at a Solution

I have already found the cross sectional area but am unsure of what to do from there.

 

[rl.bhat]

Hi Batman345, welcome to PF.
Mass per unit length μ =Density*Area

 

[kerimek]

The wave speed in a medium, such as a brass wire, can be calculated using the equation v = √(T/μ), where v is the wave speed, T is the tension, and μ is the linear density of the medium (mass per unit length). In this case, the linear density can be calculated by multiplying the density of brass (8.60×103 kg/m^3) by the cross sectional area of the wire (πr^2, where r is the radius of the wire). So, the linear density of the brass wire would be μ = (8.60×103 kg/m^3)(π(4.65×10-4 m)^2) = 0.00503 kg/m. Plugging this into the wave speed equation, we get v = √(128 N/0.00503 kg/m) = 50.5 m/s. Therefore, the wave speed in the brass wire would be approximately 50.5 m/s.