# Dimensional Analysis - waves and surface tension question

1. Mar 23, 2012

### kapitan90

1. The problem statement, all variables and given/known data

In some cases waves on deep water are driven by surface tension effects and not by gravity. The surface tension is the energy per unit area of the water surface.
The area of the water surface increases by a factor proportional to $$(Ak)^2$$ in the presence of a wave amplitude A and wavenumber k. Say whether you would expect surface tension effects to dominate over gravitational effects when the wavenumber is small or large. Give your reasons.

2. Relevant equations and the attempted solution
In the previous part of the question I found the dimension of the surface tension to be $$M*T^{-2}$$. I also found the phase velocity to be equal to $$v=c*\sqrt{\frac{y*k}{d}}$$ where y - surface tension k - wavenumber, d - density, c - some constant.

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