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enter image description here

If you throw a stone into a pond, one circle starts expanding around the centre of impact. If you pad with you hand onto the water surface continuously all 3 seconds you get many expanding circles whom all are the same distance away from the next circle and its center a new circle starts expanding each time you touch the water.
I would like to know how to realize the second kind of wave expansion.

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If you are not interested in a perfect simulation (with wave interference, variations of the speed, true collisions...), but just a quick animation, I would give a try to the Wave modifier

enter image description here

Suzanne's bust is the origin of the wave. It is animated to go up an down on the Z axis. Then the modifier's wave speed and offste was tweaked to match suzanne's frequency to give the illusion that the two effects are related.

Result:

enter image description here

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