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this unit 1.20
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group celerity

The velocity of a wave group (also known as 'group celerity')
Controller: CodeCogs



Group Celerity K

doubledepth = 0
doublegravity = 9.8066 )
Within a train of waves the movement of energy is usually slower than that of the waves. As such is you study a short train of waves they will develop at the back of the group, travel forward through the group and disappear at the front of the group.


The definition of group velocity is:

In deep water, where \inline  \omega^2=gk, group velocity is merely While in shallow water the form is a little more complicated, i.e.

Using this second form, we can plot as an example the relationship between Cg and wave-number, k :
There is an error with your graph parameters for group_celerity_k with options k=0:4 depth=1:10:4

Error Message:Function group_celerity_k failed. Ensure that: Invalid C++

Example 1

#include <stdio.h>
#include <codecogs/engineering/waves/group_celerity.h>
using namespace Engineering::Waves;
int main()
  printf("   k         Cg ");
  for(double k=0.01; k<1;k+=0.1)
    printf("\n %.6lf", k);
    double w=group_celerity_k(k,2);
    printf("  %.3lf", w);
k         Cg


kwave-number defines as (\inline  2 \pi/m). [rad/m]
depththe depth of the water to mean sea level. A value of zero or less corresponds to deep water. [m]
gravityacceleration due to gravity (default 9.8066 m/s2). [m/s2]


wave-frequency (\inline  2 \pi/s). [rad/s]


Will Bateman (February 2005)
Source Code

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Last Modified: 14 Apr 09 @ 16:38     Page Rendered: 2022-03-14 17:40:29