Deriving Power Expression for Transverse Traveling Wave

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SUMMARY

The discussion focuses on deriving the power expression for a transverse traveling wave, specifically the equation P = √(μF) * ω² * A². This equation is simplified from P = k² * ω² * F * A² * sin²(kx - ωt). The participants seek clarification on the mathematical steps involved in this reduction, indicating a potential misprint in the original derivation. The symbols used are standard in wave mechanics, ensuring the discussion is grounded in established physics principles.

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  • Understanding of wave mechanics and terminology
  • Familiarity with mathematical manipulation of equations
  • Knowledge of symbols used in wave physics (e.g., μ, F, ω, A)
  • Basic proficiency in trigonometric identities
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  • Study the derivation of wave power equations in classical mechanics
  • Learn about the role of amplitude and frequency in wave energy
  • Explore trigonometric identities relevant to wave functions
  • Investigate the implications of wave properties on energy transmission
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Students and professionals in physics, particularly those focusing on wave mechanics, as well as educators seeking to clarify wave power concepts for their curriculum.

Master J
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So in my book, it derives the expression for power in a traveling transverse mechanical wave.

P= Sqrt[(mu)F].(omega)^2.(A)^2

It reduces this from: P=k^2.omega^2.F.A^2.(sin(kx-omega.t)^2

Where all symbols are the standard ones in dealing with waves.

Could someone please go thru how it got from 2 to 1? I can't see the logic. I'm sure its obviously just basic math I am overlooking, but there may be a misprint in the derivation.

Cheers!
 
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Can you fix the equation in your threadd? I can't read the problem, sorry.
 
P=[Sqrt(uF)](w^2)(A^2)
 

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