How Does Wire Diameter Affect Wave Speed?

Thread starter freeofwork
Start date Jan 8, 2012
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Physics

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SUMMARY

The discussion centers on calculating the wave speed in two steel wires with different diameters under the same tension. The first wire has a diameter of 0.00059 meters and a wave speed of 54.0 m/s, while the second wire has a diameter of 0.00089 meters. The key formula used is v = √(F/μ), where μ represents mass per unit length, which can be derived from the wire's diameter using the formula μ = ρ * (π * d²)/4. The relationship between wave speeds in the two wires is established through the ratio v1/v2 = √(μ2/μ1).

PREREQUISITES

Understanding of wave mechanics and wave speed equations
Familiarity with mass per unit length (μ) and its calculation
Knowledge of the properties of cylindrical objects, specifically volume and density
Basic algebra for manipulating equations and ratios

NEXT STEPS

Study the derivation of wave speed equations in different mediums
Learn about the relationship between diameter and mass per unit length in cylindrical objects
Explore the concept of linear density and its applications in physics
Investigate the effects of tension on wave speed in various materials

USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators looking for teaching strategies in deriving formulas and understanding material properties.

Jan 9, 2012

freeofwork

I do not think you are a good teacher. I got the answer with the formula of v1/v2=d2/d1

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Jan 9, 2012

LawrenceC

I attempted to get you to figure the formula out because we are not permitted to merely hand out formulas and solutions. Anyone can plug into a formula and get the answer. Figuring out how to derive the formula separates the better students from the pack.