Water waves vs. other wave types

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SUMMARY

This discussion focuses on the behavior of water waves compared to other wave types, specifically sound waves and waves on strings. It establishes that as water waves approach the shore, their amplitude increases due to energy conservation, while shallow water mimics a denser medium. The participant questions the analogy with sound waves, noting that intensity relates to the bulk modulus and density, suggesting that increased density should lead to decreased amplitude. The conversation highlights the presence of dispersion in gravity surface waves, which is absent in simpler wave forms like acoustic waves.

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  • Understanding of wave mechanics and properties
  • Familiarity with concepts of amplitude and intensity
  • Knowledge of dispersion in wave equations
  • Basic principles of energy conservation in wave behavior
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  • Research the mathematical models for gravity surface waves in water
  • Explore the relationship between bulk modulus, density, and wave amplitude in sound waves
  • Study the effects of dispersion on wave propagation in different media
  • Investigate the principles of wave behavior in varying density environments
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zacman2400
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I know that as water waves get closer to shore, amplitude increases via energy conservation, and from what I have read shallow water behaves analogously to an increasingly dense medium (or at least higher index of refraction). If I try and extend this analogy to sound wave/wave on string/earthquakes in a more dense medium, I find that the amplitude should decrease. Consider the sound wave first: Intensity is proportional to square root of the bulk modulus of the material and density, it is also proportional to the square of the displacement amplitude. Assume minimal reflection between the two media. If the density increases, the amplitude should decrease somewhat..however this reasoning does not feel correct. I just need some idea of how or where my reasoning is incorrect.
 
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The equations for gravity surface waves in water contain a dispersion term, not present in simpler wave forms such as the acoustic waves you mention.
 
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