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# celerity

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

C++

## Celerity K

 doublecelerity_k( double k double depth = 0 double gravity = 9.8066 )
The velocity of a wave is defined by
$c=&space;\frac{\omega}{k}$
where ω is the wave frequency and k is the wave-number.

Using a linear linear dispersion relationship, i.e. $\inline&space;&space;w^2&space;=&space;g&space;k&space;tanh(k&space;d)$, we can derive a more useful expression for the wave velocity given a specific specific value of k, i.e.

$c&space;=&space;\sqrt&space;{&space;\frac{g}{k}&space;tanh(kd)&space;}$
In deep water (represented with d<=0), this solution reduces to
$c&space;=&space;\sqrt&space;{&space;\frac{g}{k}&space;}$

### Example 1

#include <stdio.h>
#include <codecogs/engineering/waves/celerity.h>
using namespace Engineering::Waves;

int main()
{
printf("   k         w ");
for(double k=0.01; k<1;k+=0.1)
{
printf("\n %.6lf", k);
double w=celerity_k(k,2);
printf("  %.3lf", w);
}
}
Output:
k         c
??

### Parameters

 k wave-number defines as (2π /m). [rad/m] depth the depth of the water to mean sea level. A value of zero or less corresponds to deep water. [m] gravity (default 9.8066 m/s2). [m/s2]