Hi,

I was wondering if anybody is in a position to resolve some questions about tsunami waves as they relate to the general physics of mechanical waves. I will briefly try to outline the issues:

I have some thoughts of why this might be the case, but would like to get some general feedback on the specific issue associated with energy in bullet (4) above:

I was wondering if anybody is in a position to resolve some questions about tsunami waves as they relate to the general physics of mechanical waves. I will briefly try to outline the issues:

1. The energy of a mechanical wave, i.e. one dependent on the physical interaction of the particles in the propagating medium is normally said to be proportional to the square of the amplitude of the wave.

2. Wikipedia has a page on ocean waves that gives a generalised solution of a wave’s propagation velocity: http://en.wikipedia.org/wiki/Ocean_surface_wave. However, this solution can be simplified for discussion by considering the following deep and shallow depth solutions:

[1] [tex]v = \sqrt { \frac {g\lambda}{2 \pi} } [/tex] deep water

[2] [tex]v = \sqrt { gd} [/tex] shallow water

3. Now descriptions of tsunami waves suggest that the amplitude of the wave is relatively small, e.g. 1 metre, but the wavelength is very long, e.g. 10-100km, in deep water. As such, equation [1] would suggest that these waves also move very fast.

4. However, if tsunami waves are classified as mechanical waves, they seem to conflict with the energy of the wave being proportional to the square of the amplitude.

2. Wikipedia has a page on ocean waves that gives a generalised solution of a wave’s propagation velocity: http://en.wikipedia.org/wiki/Ocean_surface_wave. However, this solution can be simplified for discussion by considering the following deep and shallow depth solutions:

[1] [tex]v = \sqrt { \frac {g\lambda}{2 \pi} } [/tex] deep water

[2] [tex]v = \sqrt { gd} [/tex] shallow water

3. Now descriptions of tsunami waves suggest that the amplitude of the wave is relatively small, e.g. 1 metre, but the wavelength is very long, e.g. 10-100km, in deep water. As such, equation [1] would suggest that these waves also move very fast.

4. However, if tsunami waves are classified as mechanical waves, they seem to conflict with the energy of the wave being proportional to the square of the amplitude.

I have some thoughts of why this might be the case, but would like to get some general feedback on the specific issue associated with energy in bullet (4) above:

5. At some level, the energy of the wave seems to be related to the volume of water displaced by the crest and trough of the wave. In the case of tsunami waves, the energy-volume is still very large, even though the amplitude is small, because the wavelength is so long.

6. As the tsunami wave approaches shallow water, equation [2] would restrict the propagation velocity is a function of the depth of the water, not its wavelength.

7. Does the amplitude of the wave grow to compensate, i.e. is this some form of conservation of energy?

8. While I assume that some wave energy must be lost to friction in shallow water, is it correct to assume, in this specific case, that the wave energy is still characterised by the volume of water displaced, i.e. is this representative of potential energy?

9. Finally, does the propagation velocity of a mechanical wave reflect some sort of notion of the kinetic energy associated with the wave? I am asking this question because a SHM wave model cycles between potential and kinetic energy maxima

Would appreciate any clarification of any of the issues raised. Thanks6. As the tsunami wave approaches shallow water, equation [2] would restrict the propagation velocity is a function of the depth of the water, not its wavelength.

7. Does the amplitude of the wave grow to compensate, i.e. is this some form of conservation of energy?

8. While I assume that some wave energy must be lost to friction in shallow water, is it correct to assume, in this specific case, that the wave energy is still characterised by the volume of water displaced, i.e. is this representative of potential energy?

9. Finally, does the propagation velocity of a mechanical wave reflect some sort of notion of the kinetic energy associated with the wave? I am asking this question because a SHM wave model cycles between potential and kinetic energy maxima

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