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Ocean and source
Change the profile, the source depth and the launch fan. Tap the water to move the hydrophone.
Layers
Model checks
The science
Ray equations
In water whose sound speed c(z) varies with depth z, a ray with angle θ from the horizontal obeys Snell's law cosθ / c(z) = constant. Written as arc-length equations: dr/ds = cosθ, dz/ds = sinθ, dθ/ds = -(cosθ/c) dc/dz, and the travel time is dt = ds / c. Rays always bend toward the region of lower sound speed, so a minimum of c(z) acts as a waveguide.
Profiles
The deep-ocean channel uses the canonical Munk profile c(z) = 1500 [1 + ε(η - 1 + e-η)], η = 2(z - 1300)/1300, ε = 0.00737, with its axis at 1300 m: rays launched near it keep crossing the axis and travel thousands of kilometres. The thermocline profile uses the Mackenzie (1981) formula with salinity fixed at 35 and an exponential temperature drop below a mixed layer. In a constant gradient g the rays are circular arcs of radius c/(g cosθ), which gives an exact test.
Honest simplifications: geometric (ray) acoustics only, so no diffraction, caustic amplitudes or frequency dependence; perfect mirror reflection at the surface and seabed with no loss or scattering; a range-independent ocean; no absorption. The ray-count plot is a qualitative proxy for intensity, not transmission loss. This is a physics demonstration of sound propagation, not a tool for locating anything.
What to try
- "SOFAR channel": the rays oscillate about the axis at 1300 m and never touch the surface.
- "Shadow zone": rays bend downward under the warm layer, leaving a region with no rays near the surface.
- "Surface duct": a cold mixed layer traps rays close to the surface.
- "Isovelocity": rays are straight lines; compare the travel-time graph.