Noise Barrier Diffraction — Acoustic Shadow Map

Barrier & Source

Barrier height H 2.5 m

Source frequency f 500 Hz

Source distance from barrier 12 m

Receiver distance from barrier 15 m

At the Receiver

Path difference δ

— m

Fresnel number N

—

Insertion loss (barrier attenuation)

— dB

—

How it works

A rigid barrier does not stop sound — it forces it to diffract over the top edge, exactly as Huygens' principle predicts for any wave meeting an obstacle. The edge acts like a secondary source, and how much energy reaches the far side depends on how much longer that bent path is than the straight line the sound would have taken without the wall.

δ = A + B − d        (path-length difference, m)
N = 2δ / λ            (Fresnel number, λ = c/f, c = 343 m/s)
IL = 5 + 20·log₁₀[ √(2πN) / tanh(√(2πN)) ]   dB   (Kurze–Anderson)

A = source-to-edge distance, B = edge-to-receiver distance, d = the direct (blocked) straight-line distance. The bar-chart map applies this formula at every point on the far side: taller H, higher frequency (shorter λ), or a receiver deep in the barrier's geometric shadow all raise N — and IL rises roughly logarithmically with it, which is why doubling a barrier's height buys far less than doubling its attenuation.

Grid bars show the modelled sound level (spreading loss − insertion loss) relative to 1 m from the source — the dip right behind the wall is the acoustic shadow zone.
The simulation assumes a barrier long compared with the source/receiver distances, the standard single-edge approximation used in traffic-noise-barrier design (ISO 9613-2 builds on the same Kurze–Anderson formula).
If the direct line from source to receiver clears the barrier top, there is no diffraction penalty — IL drops to 0 dB, shown as "clear" line of sight.

Source Receiver Barrier

Louder

Quieter

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