Acoustic Barrier Attenuation (Maekawa)
Computes how much an acoustic barrier cuts the noise reaching a receiver, using Maekawa's empirical formula, Attenuation = 10 × log₁₀(3 + 20N), where N is the Fresnel number, equal to twice the path difference divided by the wavelength — that is, N = 2 × path difference × frequency ÷ speed of sound. The path difference is the extra distance sound must travel to go over the top of the barrier instead of straight from source to receiver, and it is the only geometric input the formula needs. The result, in decibels, is what the barrier subtracts from the level that would arrive without it: with N equal to zero, meaning the receiver sits exactly on the line of sight to the top edge, attenuation is already 4.8 dB, and in practice the gain saturates between 20 and 24 dB because sound eventually flanks around the sides and passes through the panel. Since N grows with frequency, the same barrier is far more effective at high frequencies than at low ones: once N is large, every octave adds about 3 dB, which is why enclosing a compressor kills the hiss and barely touches the rumble. Enter the path difference, the frequency and the speed of sound.
Result
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Acoustic barrier: how many decibels a wall buys
The complaint arrives in decibels: a neighbour reads 58 dB(A) in the backyard and the plant room stands twenty metres away. What remains open is whether a three-metre wall settles the matter or whether the concrete goes up and nobody hears the difference. The people answering that question are environmental noise engineers, safety technicians or the site designer, usually mid-negotiation with a deadline. Guess low and the wall gets built while the complaint survives; guess high and an already costly structure gets costlier.
Maekawa measured the effect in the laboratory and fitted a curve: Attenuation = 10 × log₁₀(3 + 20N), with N, the Fresnel number, equal to 2δ ÷ λ, or 2 × δ × f ÷ c. Here δ is the path difference: add the source-to-top distance to the top-to-receiver distance, then subtract the straight line from source to receiver. It usually runs from a few centimetres to about a metre. Frequency means the offending octave band, and c is 343 m/s at 20 °C — 331 at freezing, a shift barely visible in the answer. Under 10 dB a barrier disappoints; 10 to 15 dB is the workhorse range.
The curve assumes a point source, a wall long enough to keep flanking around the ends negligible, and a panel heavy enough that whatever passes through hides under what bends over the top. Below roughly 10 kg/m² of surface density, transmission takes charge and the model loses meaning. Reflection is absent as well: between parallel facades, hand back 3 to 5 dB. Beyond a hundred metres, wind and temperature gradients bend the sound ray and can cancel the barrier outright. Unit trap: δ in centimetres inside a metres field multiplies N by a hundred.
Frequently asked questions
Where do the 13.12 dB from the defaults come from?
Why does low-frequency noise barely improve behind a wall?
Can I enter zero for the path difference?
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