About Noise Barrier Calculator (Maekawa Insertion Loss)
The noise barrier calculator predicts how many decibels a thin wall knocks off a point source using the Maekawa relation, the empirical curve from Z. Maekawa’s 1968 screen measurements that FHWA noise-barrier guidance builds on: IL = 10 log10(3 + 20N), where the Fresnel number N = 2δ/λ compares the diffraction detour δ to the wavelength. The detour comes straight from the section geometry — the ray from the source over the barrier top to the receiver, A + B, minus the direct line d — so raising the barrier or moving it closer to the source or receiver grows δ and buys more attenuation, and higher frequencies (shorter wavelengths) are blocked far more effectively than low rumble.
Enter the source height and its distance to the barrier, the barrier top height, and the receiver height and distance, pick an octave band (500 Hz is the common single-band stand-in for traffic and general noise), and the tool reports the path difference, Fresnel number, and insertion loss with an outcome badge. The test for shielding is deliberately strict: the barrier top must rise above the source-receiver sightline, and a top exactly at grazing is credited nothing — the transition zone around grazing is out of scope for the simple relation. Results are capped at 20 dB, the maximum reduction the FHWA Noise Barrier Design Handbook credits to thin walls in practice (berms rate 23 dB(A)). Add an optional source level to see the level after the barrier credit — a relative figure, not a propagation model.
How It Works
- Enter the 2-D section: source height above ground and horizontal distance to the barrier, barrier top height, and receiver height and horizontal distance beyond the barrier — in meters or feet (converted exactly at 0.3048 m/ft; the core computes in meters).
- Pick the octave band from 63 to 8000 Hz. The wavelength is λ = 343/f at 20 °C; 500 Hz is the default single-band representative for broadband sources such as traffic.
- The tool checks line of sight: the barrier top must strictly exceed the sightline height hs + (hr − hs)·ds/(ds + dr) at the barrier plane. At or below that line the outcome is "no shielding" and 0 dB — grazing incidence gets no credit.
- When the top breaks the sightline, the path difference δ = A + B − d is computed from the exact over-the-top geometry, the Fresnel number N = 2δ/λ follows, and the insertion loss is IL = 10 log10(3 + 20N), capped at the FHWA practical maximum of 20 dB for walls.
- With an optional source level entered, the tool subtracts the insertion loss to show the resulting relative level. Distance attenuation is a separate effect — chain this with the sound level distance calculator for the full picture.
Worked Example
A pump (source) 1.5 m above grade stands 10 m from a proposed 4 m wall; the listener is 20 m beyond the wall, also at 1.5 m. Over the top, A = √(10² + 2.5²) = 10.308 m and B = √(20² + 2.5²) = 20.156 m; the direct line between the equal-height points is d = 30 m, so the detour is δ = 10.308 + 20.156 − 30 = 0.463 m. At 500 Hz the wavelength is 343/500 = 0.686 m, giving N = 2 × 0.463/0.686 = 1.351 and IL = 10 log10(3 + 20 × 1.351) = 10 log10(30.02) = 14.8 dB — shielded, well under the 20 dB cap. The same wall at 4000 Hz gives N = 10.81 and a raw 23.4 dB, so the credited loss is capped at 20 dB. With an 80 dB source level, the 500 Hz result is 80 − 14.8 = 65.2 dB.
Formulas
- Maekawa insertion loss (point source)
IL = 10 log10(3 + 20 N), capped at 20 dB- Fresnel number
N = 2 delta / lambda, lambda = c / f, c = 343 m/s- Path difference from the section geometry
delta = A + B - d; A = sqrt(ds^2 + (hb-hs)^2), B = sqrt(dr^2 + (hb-hr)^2), d = sqrt((ds+dr)^2 + (hr-hs)^2)- Line-of-sight break test (strict)
shielded only if hb > hs + (hr - hs) * ds / (ds + dr)- Resulting relative level (optional)
L_after = L_source - IL
Standards & References
- Maekawa, Z., "Noise reduction by screens", Applied Acoustics 1 (1968) 157-173
- Kurze, U.J. & Anderson, G.S., "Sound attenuation by barriers", Applied Acoustics 4 (1971) -- the 10 log10(3 + 20N) codification
- FHWA Noise Barrier Design Handbook, Sec. 3 Acoustical Considerations -- N = 2(delta/lambda); practical maxima 20 dB(A) thin walls, 23 dB(A) berms
Frequently Asked Questions
How much noise reduction does a barrier wall actually give?
A wall that just breaks the line of sight starts near the theoretical 5 dB floor (10 log10(3) = 4.77 dB in the Maekawa relation), and every extra meter of height beyond the sightline adds roughly 1.5 dB in typical highway geometry. Well-designed walls deliver 10 to 15 dB in practice, and the FHWA Noise Barrier Design Handbook treats about 20 dB(A) as the realistic maximum for thin walls, which is why this calculator caps the credited loss there.
What is the Fresnel number and why does it drive everything?
The Fresnel number N = 2δ/λ compares the extra distance sound must travel over the barrier top (δ) to the wavelength (λ = 343/f). It is the single parameter in the Maekawa relation: the same wall shields high frequencies far better than low ones because a fixed detour is many wavelengths at 4 kHz but a small fraction of one at 63 Hz. Doubling the frequency doubles N, which adds about 3 dB once N is large.
Why does the calculator show 0 dB when the barrier just reaches the sightline?
The tool requires the barrier top to rise strictly above the source-receiver sightline before crediting any shielding. Real diffraction is continuous — attenuation grows smoothly through the grazing zone, and the Maekawa curve itself gives about 5 dB at grazing — but modeling that transition zone honestly requires more than the simple point-source relation, so this calculator deliberately credits nothing until line of sight is truly broken. That is also why the result jumps from 0 to 4.77 dB (the δ → 0⁺ limit of 10 log10(3)) as the top clears the line.
Where should a noise barrier be placed for the best result?
As close as possible to either the source or the receiver — the worst position is midway. The path difference δ = A + B − d grows when the over-the-top angles get steep at one end, which happens when the wall hugs the source or the listener. Try it in the calculator: with source and receiver 30 m apart and a 4 m wall, sliding the wall from the middle toward either end visibly raises the Fresnel number and the insertion loss.
Does the resulting level include distance attenuation?
No. When you enter an optional source level, the calculator simply subtracts the insertion loss — it is the level you would have had at the receiver without the barrier, minus the barrier credit. Spreading loss with distance, air absorption, and ground effects are separate mechanisms; use the sound level distance calculator to project a measured level to the receiver position first, then apply the barrier insertion loss from this tool to that figure.
Is an earth berm better than a wall of the same height?
Generally yes. FHWA guidance credits berms with a higher practical maximum — 23 dB(A) versus 20 dB(A) for thin walls — and field practice attributes an extra 1 to 3 dB(A) to the berm’s soft, absorptive top and flanks compared with a hard-edged thin wall of equal height. This calculator models the thin-wall case; treat its result as a slightly conservative estimate for a berm of the same crest height, and remember a berm needs far more right-of-way width.