Mechanical Water Waves: Understanding Behavior

[Wxfsa]

I want to understand how water waves behave. I do not need to be able to solve them (although i would like a derivation) because I tried hard to find it but I were not able to find any source on it (i probably didn't know the terms i should have been searching for)

The type of stuff I want to learn are (some example situations) (ignoring losses) wavefunctions of time:
-what if a rod is moved periodically, vertically in water (cylinderical waves)
-what if the rod is moved for a single period
-what if a long plate is moved horizontally (so waves in two opposite directions)

 

[tech99]

I want to understand how water waves behave. I do not need to be able to solve them (although i would like a derivation) because I tried hard to find it but I were not able to find any source on it (i probably didn't know the terms i should have been searching for)

The type of stuff I want to learn are (some example situations) (ignoring losses) wavefunctions of time:
-what if a rod is moved periodically, vertically in water (cylinderical waves)
-what if the rod is moved for a single period
-what if a long plate is moved horizontally (so waves in two opposite directions)

I want to understand how water waves behave. I do not need to be able to solve them (although i would like a derivation) because I tried hard to find it but I were not able to find any source on it (i probably didn't know the terms i should have been searching for)

The type of stuff I want to learn are (some example situations) (ignoring losses) wavefunctions of time:
-what if a rod is moved periodically, vertically in water (cylinderical waves)
-what if the rod is moved for a single period
-what if a long plate is moved horizontally (so waves in two opposite directions)

1. The rod creates a cylindrical wave, where the amplitude depends on time and radius. The wave spreads in two dimensions only, so the energy is spread around the circumference, and the energy density falls off as 1/radius. Therefore the amplitude falls off inversely with the square root of radius.
2. If a rod is moved for a single period, the water particles would have to go from stationary to a finite velocity in zero time, requiring infinite acceleration, so I do not think a wave will be produced.
3. A long plate produces a beam which is initially parallel, so the amplitude will not fall off with distance. The radiation from each side of the plate is in anti phase. (At long distances the beam diverges, so the decay becomes similar to the cylindrical wave).