Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Waves in water

  1. Dec 14, 2004 #1
    for shallow waves (where [tex]\lambda \leq 1/2 depth[/tex]) in a tub, can anyone tell me why.....

    [tex]speed\ of\ wave = \sqrt{gravity * depth}[/tex]

    i mean, is there a way to get this formula by deriving from others?
  2. jcsd
  3. Dec 14, 2004 #2
    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 [Broken]
    Last edited by a moderator: May 1, 2017
  4. Dec 14, 2004 #3


    User Avatar
    Science Advisor
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook