Noise Barrier Insertion Loss (Fresnel Number)

The insertion loss follows Maekawa's relation from the Fresnel number, twice the path difference over the wavelength, where the path difference is how much farther sound travels over the top than straight through. Two consequences matter more than barrier height. FREQUENCY decides the answer: a half-foot path difference is 13 dB at 1,000 Hz and 7 dB at 125 Hz, because a long wavelength diffracts around the top and a short one does not. Tyre noise lives at the high end and is substantially reduced; truck exhaust and engine rumble live at the low end and are barely touched, which is exactly what residents report after a barrier goes in -- the traffic sounds different and the loud part is still there. Reporting one A-weighted number hides this. And BREAKING THE LINE OF SIGHT IS A THRESHOLD, NOT A SLOPE: a barrier that just grazes the sight line has a Fresnel number of zero and an insertion loss of 10 log10(3), about 4.8 dB, which is essentially nothing. There is no partial credit for a barrier you can see over. Flanking caps it in practice, because sound goes around the ends and a driveway gap is a hole most of the benefit leaves through, which is why the practical ceiling is 20 to 25 dB regardless of height. A single-barrier, single-frequency, point-source screen: it does not address ground effect, atmospheric absorption, reflections from a parallel barrier or facade, multiple diffraction over a thick barrier or berm, source spectrum and directivity, the barrier material's own transmission loss, or structural design. The applicable highway agency noise procedure, the acoustical consultant, and the governing ordinance govern.

Maekawa's barrier attenuation relation: insertion loss = 10 log10(3 + 20 N), where the Fresnel number N is twice the path difference over the wavelength, and the wavelength is the speed of sound (taken as 1,130 ft/s at room temperature) over the frequency.

A single-barrier, single-frequency, point-source screen. It does not address ground effect, atmospheric absorption, reflections from a parallel barrier or a facade on the far side, multiple diffraction over a thick barrier or a berm, the source's actual spectrum and directivity, the transmission loss of the barrier material itself, or barrier structural design and wind loading. Flanking around the ends caps a real barrier near 20 to 25 dB regardless of what the geometry alone would give.

One logarithm from a published empirical relation; no proprietary chart is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: path_difference_ft, source_to_top_ft, top_to_receiver_ft, source_to_receiver_ft, frequency_hz, second_frequency_hz, practical_ceiling_db, wavelength_ft, fresnel_number, raw_insertion_loss_db, second_insertion_loss_db, grazing_db

• Single frequency, single barrier a real source has a spectrum and a real site has flankingthe acoustical consultant
• The material transmits less than it diffracts otherwise transmission through the barrier governs insteadthe barrier manufacturer's data
• A practical ceiling applies flanking caps a real barrier near 20 to 25 dBthe applicable highway agency noise procedure