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EDIT: From Robin Betts suggestion as to reflections, it's relatively easy to add a 'hard edge' to the grid where the vertexes are fixed - and this results in reflections from the boundary. This can be achieved by using the Total output of the Edges of Vertices node - as this will be 4 for any vertex in the bulk of the grid and less than 4 for any edge or corner vertex (which will be missing one or more neighbours) - see the selected nodes in the following image :

This results in the wave being reflected from the edge :

Notice how the circular wave is reflected (upside down) behind the main wavefront.

EDIT : Just to prove that it's possible to affect this based on mesh proximity, here's a bit of a dirty hack to the nodes to use the position of another mesh (animated to collide with the surface) to affect the velocity of the grid :

You can add some damping to the motion by adding a Multiply node before storing the new Velocity - eg, to multiply by 0.99 to damp the velocity by 1% each step. This will calm the motion over time. Here's the final result :

You can add some damping to the motion by adding a Multiply node before storing the new Velocity - eg, to multiply by 0.99 to damp the velocity by 1% each step. This will calm the motion over time. Here's the final result with increased grid resolution :