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COST (GBP)
this unit 1.20
sub units 0.00
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group celerity

The velocity of a wave group (also known as 'group celerity')
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Interface

C++
HTML

Group Celerity K

Group Celerity K Calculator
 
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doublegroup_celerity_kdoublek
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.

[DIAGRAM]

The definition of group velocity is:

In deep water, where \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 :
\graph  k=0:4, depth=1:10:4, gravity=9.8066

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);
  }
}
Output:
k         Cg
??

Parameters

kwave-number defines as (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]

Returns

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

Authors

Will Bateman (February 2005)
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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