Question

If you drop a stone into a pond and generate an initial wave height of say one inch, what equations apply to calculate the wave height at various distances out, say 10 feet or 20 feet. I understand the height of a wave crest diminishes in inverse proportion to the square root of its distance from its origin, but am unclear about the nature of the equation. Density for fresh water versus salt water, etc may be a factor. Thanks.

Answer 1

height of a wave crest diminishes in inverse proportion to the square root of its distance from its origin, but am unclear about the nature of the equation
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Amplitude = constant/(root(distance)) where the constant depends on the particular system - water fresh or salt; or something like glycerine which may not generate a wave at all.

my reflex response here would be that the amplitude of the wave would decrease exponentially (e=2.7 ish), wherein there is a "characteristic length" (time constant were the exponential to be in time). If memory serves, after 5 time constants the steady state prevails, and I guess that in this case that would mean that the oscillations would have "stopped".
Is the name "Agua" linked to "AQua"

Answer 2

I live in Texas. Aqua is Spanish for water.

Answer 3

Si yo comprendo, e io capisco.
Muchas gracias, e grazie

Answer 4

have a look, specimen:



using:
\(y\ =\ A\frac{1}{\sqrt{x}}\sin \ x\)

this is like a freeze-frame in time.