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

Contents

Interface Function Documentation Page Comments

Interface

#include <codecogs/engineering/waves/celerity.h>

using namespace Engineering::Waves;

double

celerity_k (double k, double depth=0, double gravity=9.8066) Uses a linear dispersion relationship to compute wave velocity

Function Documentation

The velocity of a wave is defined by where ω is the wave frequency and k is the wave-number.

Using a linear linear dispersion relationship, i.e. , we can derive a more useful expression for the wave velocity given a specific specific value of k, i.e.

In deep water (represented with d<=0), this solution reduces to

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/s^2). [m/s^2]

Returns:

wave-frequency (2π /s). [rad/s]

Authors:

Will Bateman (February 2005)