I have forgotten

• https://me.yahoo.com
COST (GBP)
1.20
0.00
0

# group celerity

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

C++
HTML

## Group Celerity K

Group Celerity K Calculator

Add calculator to website or email

 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/s2). [m/s2]

### 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.

Not a member, then Register with CodeCogs. Already a Member, then Login.