Noise Barrier Diffraction 2D — Acoustic Wave Field Simulator

Barrier & Source

Barrier height H 2.5 m

Source frequency f 300 Hz

Source distance from barrier 8 m

Receiver distance from barrier 8 m

At the Receiver (measured from the field)

RMS pressure (barrier)

—

RMS pressure (no barrier)

—

Measured insertion loss

— dB

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How it works

Instead of plugging distances into the Kurze-Anderson formula, this version numerically solves the 2D acoustic wave equation with a finite-difference time-domain (FDTD) scheme, on a vertical slice through the road: x = distance from the barrier, y = height above ground. The barrier and the ground are rigid reflectors; the domain edges use a first-order Mur absorbing boundary so the wave leaves the simulated region instead of bouncing back.

∂²p/∂t² = c²∇²p            (2D scalar wave equation, c = 343 m/s)
p[i,j]ⁿ⁺¹ = 2p[i,j]ⁿ − p[i,j]ⁿ⁻¹ + (cΔt/Δx)²·∇²p[i,j]ⁿ
rigid wall: mirror the wall-side neighbour (∂p/∂n = 0)
IL = 20·log₁₀( RMS_no-barrier / RMS_barrier )   — measured live at the receiver cell

A second, invisible reference grid runs the identical source with no barrier in it, purely so the receiver's measured level can be compared against the free-field case — the insertion loss you see is read directly off two simulated wave fields, not computed from geometry. The visible field also includes the ground bounce, so at some frequencies you'll see the barrier briefly look less effective than a smooth formula would predict — that's real interference between the diffracted and ground-reflected paths, not a bug.

The colour field is instantaneous acoustic pressure: blue = compression, red = rarefaction (sign flips every half-period).
Grid spacing (0.15 m) resolves the low end of the frequency range comfortably; near 500 Hz the wave is coarsely resolved (~4-5 points per wavelength), which is why the field looks a little more jagged at high frequency — a genuine numerical-dispersion trade-off of any FDTD grid, not a rendering artefact.
Taller barrier or higher frequency → larger Fresnel number → deeper measured shadow, exactly as in the 3D single-edge model, but here that shadow emerges from the simulated wavefronts bending around the edge (Huygens' principle in action) rather than being assumed by a formula.

Source Receiver Barrier

−p