Propagation Velocity of Transverse Waves

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SUMMARY

The propagation velocity of transverse waves in a steel wire can be calculated using the formula Cw = sqrt(Tension / linear mass density). Given a steel wire with a radius of 0.65 mm and a tension of 11.29 N, the first step is to convert the volume mass density of steel (7800 kg/m³) to linear mass density. This involves calculating the cross-sectional area of the wire and determining the mass of one meter of the wire to find the linear mass density.

PREREQUISITES
  • Understanding of wave propagation principles
  • Knowledge of linear mass density calculations
  • Familiarity with tension and its effects on materials
  • Basic geometry for calculating cross-sectional areas
NEXT STEPS
  • Calculate the cross-sectional area of the steel wire using the formula A = πr²
  • Convert the volume mass density of steel to linear mass density using the formula μ = ρ × A
  • Apply the formula Cw = sqrt(Tension / linear mass density) to find the wave velocity
  • Explore the effects of different materials on wave propagation velocities
USEFUL FOR

Students and professionals in physics, engineering, and materials science who are studying wave mechanics and the properties of materials under tension.

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A steel wire of radius 0.65 mm is subject to a tension of 11.29 N. Steel has a volume mass density of 7800 kg/m3. Find the velocity of propagation of transverse waves on this wire, in m/s.

I found the cross sectional area of the wire but I am not sure where to go from there. I know I need to convert the volume mass density to linear mass density so I can use the formula
Cw=sqrt(Tension/linear mass density).
 
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Find the volume of one meter of the wire, then its mass.
 
Thank You
 

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