That depends on a number of factors. Ripples are capillary waves, whose dispersal rate can be calculated mathematically. The formula is this:
In this equation, ω is the angular frequency (the measure of how fast the energy causing the ripple is moving), σ the surface tension of the water, ρ the density of the heavier water, ρ’ the density of the lighter water and k the number of wavelengths per unit distance. Sound complicated? It is. Suffice it to say that, while you can calculate the distance a ripple will travel mathematically if you know all the variables, in practical effect it depends on how big the lake is, the density of the water (is a fresh or salt lake? is it cold or warm?) and the force of what caused the ripple in the first place, such as a stone being thrown into the water or a boat engine moving.
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