# group celerity

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

Controller: **CodeCogs**

doublegroup_celerity_k( | double | k | |

double | depth` = 0` | ||

double | gravity` = 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 , 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*:### 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

k wave-number defines as (). [rad/m] depth the depth of the water to mean sea level. A value of zero or less corresponds to deep water. [m] gravity acceleration due to gravity (default 9.8066 m/s ^{2}). [m/s^{2}]

### Returns

- wave-frequency (). [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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