Formula

Received level (ISO 9613-2)

\[ L_p = L_W + D_c - (A_{div} + A_{atm} + A_{gr} + A_{bar}) \]

What the symbols mean

L_p — received sound pressure level (dB)
L_W — source sound power level (dB)
D_c — source directivity correction (dB)
A_div — geometrical divergence attenuation (dB)
A_atm — atmospheric absorption attenuation (dB)
A_gr — ground-effect attenuation (dB)
A_bar — barrier / diffraction attenuation (dB)
δ — path-length difference of the diffracted ray (m)
N — Fresnel number, N = 2δ/λ (dimensionless)

Inputs

Geometry

Source height (m)

Receiver height (m)

Horizontal distance source → receiver (m)

Barrier present

Barrier height (m)

Distance source → barrier (m)

Automatically size the barrier to reach a target insertion loss

Ground type

Atmospheric conditions

Temperature (°C)

Relative humidity (%)

Sound power Lw (dB per octave)

Source spectrum

Hz	63	125	250	500	1k	2k	4k	8k
dB

Result

Received level (with barrier)—

Level without barrier—

Barrier insertion loss—

Diagram (cross-section)

Show dimensions

Received level per octave band

Understand the theory — diffraction, barrier and propagationinteractive

An acoustic barrier does not "block" sound: it forces it to bend around its top edge. The sound then takes a small detour to reach the receiver, and it is this detour — the path-length difference \(\delta\) — that creates the attenuation. The taller the barrier (or the lower and closer the source and receiver are to it), the larger \(\delta\), and the more effective the barrier. Because \(\delta\) is compared to the wavelength, a barrier always attenuates high frequencies far better than low ones. Raise the barrier below and watch the attenuation climb.

As long as the barrier does not break the source–receiver line of sight, it does almost nothing. Once it does (receiver in the "shadow zone"), attenuation starts near 5 dB and grows with height. In practice a thin barrier is capped at ~20 dB (single screen): beyond that, sound passing through or around the sides takes over.

Diffraction, path difference and Fresnel number

The direct source → receiver ray has length \(d\). With a barrier, sound goes over the top edge: it travels \(d_{ss}\) (source → top) then \(d_{sr}\) (top → receiver). The path-length difference is the imposed detour:

\[ \delta = (d_{ss} + d_{sr}) - d \]

It is compared to the wavelength through the Fresnel number \(N = 2\delta/\lambda = 2\delta f/c\). The barrier attenuation then follows Maekawa's empirical formula (here in the Kurze-Anderson form), starting at ~5 dB at grazing incidence (\(\delta = 0\)) and growing with \(N\):

\[ A_{bar} = 5 + 20\log_{10}\!\left( \dfrac{\sqrt{2\pi N}}{\tanh\sqrt{2\pi N}} \right), \quad N = \dfrac{2\delta}{\lambda} \]

In ISO 9613-2 this attenuation is written \(D_z = 10\log_{10}(3 + (C_2/\lambda)\,C_3\,z\,K_{met})\), where \(z\) is the path difference, \(C_2 = 20\) folds in the ground effect, \(C_3 = 1\) for a single screen and \(K_{met}\) corrects for weather. The effect is capped at 20 dB (single) or 25 dB (double).

The ISO 9613-2 propagation chain

The barrier is just one term among several. The received level is built from the source power \(L_W\) by subtracting every attenuation encountered:

\[ L_p = L_W + D_c - (A_{div} + A_{atm} + A_{gr} + A_{bar}) \]

A_div — geometrical divergence — the wave spreads as a sphere: −6 dB per doubling of distance, \(A_{div} = 20\log_{10}(d) + 11\).
A_atm — atmospheric absorption — air turns sound into heat (ISO 9613-1); negligible in the bass, strong in the treble and over long distances.
A_gr — ground effect — reflection and absorption by the ground, depending on its porosity (factor \(G\): 0 hard, 1 soft) and the source/receiver heights.
A_bar — barrier — the diffraction described above; when a barrier acts, it replaces the ground term (folded into \(C_2\)).

Ground effect: hard ground can amplify

Over hard ground (road, water) the reflected wave adds to the direct wave: the level can rise by a few dB (\(A_{gr}\) negative). Over soft ground (grass, soil), interference instead creates a marked attenuation dip around 250–500 Hz when source and receiver are low. ISO 9613-2 computes this through three regions (source side, middle, receiver side), each weighted by its \(G\) factor.

Limits of a real barrier

Flanking around the sides: a too-short barrier lets sound past its ends. It must extend well beyond the protected zone.
Transmission through: the panel must be heavy enough (mass law) so the transmitted sound stays 10 dB below the diffracted sound.
Reflections: between two parallel barriers (road cutting), repeated reflections (the "canyon effect") degrade performance; the face is then treated with an absorber.
Weather: with downwind or temperature inversion, rays bend toward the ground and "pass over" the barrier; hence the \(K_{met}\) correction.
Double diffraction: a wide berm or a building diffracts on two edges; the simple model then underestimates the attenuation.

Worked examples

Situation	Effect	Reading
2 m barrier, receiver 4 m at 50 m	IL ≈ 6–9 dB(A)	the barrier barely breaks the line of sight
4 m barrier, receiver 4 m at 50 m	IL ≈ 15 dB(A)	clear shadow zone, good road barrier
1 m barrier (high receiver)	IL ≈ 0 dB	receiver in the lit zone
Hard ground, no barrier	A_gr ≈ −3 dB	reflection reinforces the level

Common mistakes

Believing a barrier "cuts" sound: it only forces it to diffract.
Sizing a barrier without checking it actually breaks the target receiver's line of sight.
Forgetting transmission through the panel (too light) or flanking around the sides.
Expecting the same performance in the bass as in the treble.
Neglecting the ground effect: over hard ground the no-barrier level may already be amplified.

Sources : Z. Maekawa, Noise reduction by screens, Applied Acoustics (1968); U. J. Kurze & G. S. Anderson, Sound attenuation by barriers (1971); ISO 9613-1 (atmospheric absorption); ISO 9613-2 (attenuation of sound during outdoor propagation); CNOSSOS-EU:2015.