# At the ocean surface, why do large amplitude waves travel faster than small amplitude waves?

I understand the mathematics behind it but I am looking for an intuitive description.

• Classical waves exhibit frequency dispersion, but not amplitude dispersion (that I'm aware about .) I assume you are asking about real waves (non-linear and non-classical.) Can you please explain what leads you say large amplitude waves travel faster than small amplitude waves? – Mark Rovetta Jun 27 '15 at 5:30
• yes I am talking about solitary waves. See Russell $c = \sqrt{g(d+a)}$ where $a$ is the wave amplitude and $d$ is the depth. – reddit Jun 27 '15 at 5:34
• "The properties of a solitary waves result from an exact balance between dispersion which tends to spread the solitary wave into a train of waves, and non-linear effects which tend to shorten and steepen the wave." Is from here: oceanworld.tamu.edu/resources/ocng_textbook/chapter16/… – Mark Rovetta Jun 28 '15 at 16:36
• @reddit: maybe you should add that equation and the reference for it to your question? – naught101 Mar 29 '16 at 1:48
• This seems like a geophysics/fluids question and is therefore appropriate here. Even the book cited is a "Physical Oceanography" book. I am curious to see an answer for this. – Antonio Apr 4 '16 at 3:30

## 2 Answers

Higher amplitude waves, on water, are caused by larger disturbances and longer durations of energy input, in the form of wind, than smaller ones. Quite simply in order to build a big ocean wave you need to put in a lot of acceleration of surface waters over an extended period of time. So it's not just that the wave itself is travelling that much faster, the whole surface that the wave is moving on is itself moving in the same direction as the wave on the surface. The larger amplitude of the waves is in fact partly due to them going faster rather than the other way around.

NB: This doesn't apply with Tsunami waves as those are full column disruptions involving the water column from seabed to wave crest.

• When ocean waves travel away from the generation zone they may enter regions of calm ocean with no significant background currents. At these locations high amplitude waves still travel faster than low amplitude waves. – Isopycnal Oscillation Sep 6 '17 at 16:59

This falls under the basic principles of physics - the higher the amplitude, the more energy. The ocean is the material that is being used, but think of it as an isolated wave of energy. Under any application - light, sound, etc - the higher the amplitude a/o frequency, the more energy. More energy = more speed.

• Think you've made a mistake. Frequency and amplitude aren't related in the classical basic wave definition for a single wave. You say higher amplitude = more energy = more speed. Yet light can have varying amplitudes (brightnesses)... and still has the same speed. Likewise with sound waves. I don't know much about water waves, but your answer fails for some of the other types you note. More energy does not necessarily mean faster wave propagation, as in longitudinal waves like light/sound, it can simply mean more motion normal to its translation (meaning higher amplitude). – JeopardyTempest Feb 10 '17 at 17:56