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

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Interface

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

using namespace Engineering::Fluid_Mechanics::Waves;

double celerity_k(double k, double depth=0, double gravity=9.8066)

The velocity of a wave is defined by

$c= \frac{\omega}{k}$

(1)

where ω is the wave frequency and k is the wave-number.

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

$c = \sqrt { \frac{g}{k} tanh(kd) }$

(2)

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

$c = \sqrt { \frac{g}{k} }$

(3)

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

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]

Interactive Calculator

depth

gravity

Result –