Velocity of longitudinal waves in a solid.

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SUMMARY

The discussion focuses on the velocity of longitudinal waves in solids, specifically addressing the equation for wave velocity, c = √(springiness/massiness). The participants clarify that for longitudinal waves, massiness corresponds to density (ρ), while springiness relates to the bulk modulus (B) of the solid. The bulk modulus is defined in Pascals (N/m²) and is crucial for understanding wave propagation in solids, contrasting with the behavior of gases.

PREREQUISITES
  • Understanding of wave mechanics and wave velocity equations
  • Familiarity with the concepts of density (ρ) and bulk modulus (B)
  • Knowledge of Newton's laws and units of pressure (Pascals)
  • Basic principles of solid mechanics and material properties
NEXT STEPS
  • Study the relationship between bulk modulus and wave velocity in solids
  • Learn about longitudinal and transverse wave propagation in different media
  • Explore the derivation of wave equations in solids and their applications
  • Investigate the physical significance of the bulk modulus in material science
USEFUL FOR

Physics students, material scientists, and engineers interested in wave propagation in solids and the underlying principles of elasticity and density.

RazerM
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Homework Statement


Our lecturer gave us a general equation for velocity of waves; (where c= wave velocity)
c= \sqrt{\frac{\textrm{springiness}}{\textrm{massiness}}}
(Excuse the terms, I'd personally rather have been given the equations here..)

So for transverse waves on a string/wire (where T= Tension and \mu= mass per unit length)
c= \sqrt{\frac{T}{\mu}}
and for longitudinal waves in a gas (whereB_{ad}= the adiabatic bulk modulus and \rho= density)
c= \sqrt{\frac{B_{ad}}{\rho}}


Where I am stuck is longitudinal waves in a solid, I'm assuming massiness = \rho but am unsure about springiness.

Homework Equations


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The Attempt at a Solution


So for longitudinal waves in a solid; solving for the dimensions of springiness appears to show that springiness is in Newtons but how does Force correlate to a wave through a solid, or am I missing the point completely?
 
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hmm, I think you made a mistake in that unit calculation. I get Pascals (N/m^2), a unit of pressure... but I'm not sure what physical quantity that corresponds to, since solids don't really have pressure in the same sense as gasses. This is a particular area of physics in which my knowledge is sadly lacking.

Isn't there a bulk modulus for solids?
 

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