Deriving the Speed of Shallow Wave Formulas

[ph_low]

for shallow waves (where $$\lambda \leq 1/2 depth$$) in a tub, can anyone tell me why...

$$speed\ of\ wave = \sqrt{gravity * depth}$$

i mean, is there a way to get this formula by deriving from others?

 

[da_willem]

It can (ofcourse) be derived from the Navier-Stokes equations. See e.g. http://www.ocean.washington.edu/people/faculty/parsons/OCEAN549B/lwt-lect.pdf

 

[Clausius2]

for shallow waves (where $$\lambda \leq 1/2 depth$$) in a tub, can anyone tell me why...

$$speed\ of\ wave = \sqrt{gravity * depth}$$

i mean, is there a way to get this formula by deriving from others?

That comes from the Shallow Waters Equations. These equations are a version of Navier-Stokes equations for small waves into water whose amplitude is small compared with the height of water itself.

The Shallow Waters Equations are also very similar (mathematically) to the ones of the Linear Acoustics. If you want to know more about that, you will have to pay attention to derivation, as DaWillem has said. I don't know a rapid method.