The Wave Equation in Polar Coordinates and 3D Modeling of Waves

For this project we took the wave equation, which is a partial derivative equation that includes variables of time, space and velocities of the waves. We then took the equation in cartesian coordinates (x,y,z) and converted it into polar coordinates (⍴,ɸ,𝛳) to express the angular motion of waves better in a 3 dimensional model. We used the wave equation in polar coordinates to describe three types of waves in water.

  1. Waves from a water droplet
  2. Waves from a ship moving through water
  3. Waves from moving water

Once we found the equations, we found models of the waves on mathematica and used those codes to model our own examples. These models respectively took into consideration the decreasing amplitudes and increasing distance between peaks of the waves, and the changing position of the ship and the waves that are generated from this motion, and finally the velocities of unbounded waves which depend primarily on the source of movement.

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