How Does Tsunami Wavelength Affect Particle Displacement and Wave Equation?

In summary, the conversation discusses the wavelength of a tsunami, which propagates as a sinusoidal plane wave towards shore. The question then asks to determine the peak value of horizontal particle displacement and whether it is consistent with the assumption of mainly horizontal water momentum. Another question asks for a rederivation of the wave equation in terms of amplitude, taking into account nonconstant equilibrium depth. The person asking for help is unsure of how to approach the derivation and is seeking assistance.
  • #1
snickersnee
34
0

Homework Statement


Wavelength of a tsunami:
upload_2015-9-19_16-35-28.png


Propagates toward shore as a sinusoidal plane wave.
- determine the peak value of the horizontal particle displacement. Is your answer consistent with the assumption that the water momentum is mainly horizontal? Explain by considering the magnitude of the ratio uz/ux (vertical/horizontal components of particle velocity)

- rederive the wave equation in terms of zeta (amplitude) allowing for nonconstant equilibrium depth h_0

Homework Equations



upload_2015-9-19_21-19-29.png
[/B]
Wave equation
upload_2015-9-19_21-7-31.png

The Attempt at a Solution


[/B]
I thought the horizontal displacement would just be the wavespeed times the period but that would just give the wavelength so that couldn't possibly be right. As for deriving the wave equation, I don't even know where to start on that one. Any help would be appreciated
 
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  • #2
Have you derived wave equation before?
 

FAQ: How Does Tsunami Wavelength Affect Particle Displacement and Wave Equation?

1. What is the wave equation for a tsunami?

The wave equation for a tsunami is a mathematical formula that describes the propagation of a long ocean wave caused by a sudden disturbance, such as an earthquake or volcanic eruption.

2. How is the wave equation for a tsunami derived?

The wave equation for a tsunami is derived from the fundamental laws of fluid dynamics, including the principles of conservation of mass, momentum, and energy. It takes into account the depth and shape of the ocean floor, as well as the properties of water, to accurately model the behavior of a tsunami wave.

3. What are the variables in the wave equation for a tsunami?

The variables in the wave equation for a tsunami include the wave height, wavelength, wave speed, and water depth. These variables can vary depending on the characteristics of the tsunami, such as the magnitude of the earthquake or the location of the disturbance.

4. Can the wave equation for a tsunami predict the size and impact of a tsunami?

Yes, the wave equation for a tsunami can be used to predict the size and impact of a tsunami. By inputting data on the characteristics of the disturbance and the geography of the affected area, scientists can use the wave equation to predict the height and speed of the tsunami wave, as well as its potential impact on coastal regions.

5. How accurate is the wave equation for a tsunami?

The accuracy of the wave equation for a tsunami depends on the quality and completeness of the input data. With accurate and up-to-date information, the wave equation can provide a fairly accurate prediction of the size and impact of a tsunami. However, it is important to note that there are always uncertainties and unpredictable factors in natural phenomena, so the predictions should be used as a guide rather than absolute certainty.

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