How to Retrace the Path of Oncoming Waves

Wave path is a function of several physical factors.

Anyone who's visited the beach is familiar with the effect of a wave. However, the physical principle underlying ocean waves manifests itself in many forms. A wave is the transfer of energy through matter without permanently displacing that matter. This fact is apparent in the effect of ocean waves: The water is jolted up and down but comes to rest at more or less the same position, as the wave energy carries onward toward the shore. You can use a derivation of the wave formula, (∂^2u)/(∂t^2) = ∇c^2(u), to trace the path of oncoming waves.

Instructions

1. Input the value of u, which is the frequency of the wave.

2. Determine the duration, t, for which you want to trace the wave path.

3. Calculate ∂, the partial derivative, based on Steps 1 and 2, wherein ∂u/∂t is equal to f(u) or ∂^2 + ∂u + u^2.

4. Input the value of c, the wave's amplitude (the distance between its crest and its trough, or its highest and lowest points as it moves through space.)

5. Solve for ∇, which is the Laplatian operator, a differential operator used in physics. To solve, isolate ∇ by dividing both sides by c^2(u). The result is the mathematical expression of the wave path.

References

• Physics of Waves; William Elmore; 1985