Propagation of Outdoor Sound - Partial Barriers

Calculate the Fresnel number and barrier attenuation for outdoor sound propagation around partial barriers. Determines how sound is affected by reflection, transmission, and diffraction around barriers.

Fresnel Number & Barrier Attenuation Calculator

When a barrier is interposed between a sound source and a receiver, sound propagates through three mechanisms:

Reflection back from the barrier
Transmission through the barrier
Diffraction around the barrier

The attenuation is expressed using the Fresnel number:

N = 2δ / λ

Where:

N = Fresnel number (dimensionless)
δ = A + B - d (path difference in meters or feet)
λ = wavelength of the sound (meters or feet)

Key Points:

High frequencies (short wavelengths) produce higher Fresnel numbers and greater attenuation
Low frequencies (long wavelengths) produce lower Fresnel numbers and less attenuation
Attenuation is reduced for moving sources (vehicles) compared to stationary sources

Calculator

Inputs

Distance A (source to barrier top) (m)

Distance B (barrier top to receiver) (m)

Distance d (source to receiver direct) (m)

Sound Frequency (Hz)

Wavelength (m)

Results

Path Difference (δ)-- m

Fresnel Number (N)--

Estimated Barrier Attenuation-- dB

Example Calculation

Given:

Distance A = 20 m (highway to barrier top)
Distance B = 30 m (barrier top to person)
Distance d = 43 m (highway to person direct)

For 500 Hz noise (λ = 0.69 m):

δ = 20 + 30 - 43 = 7 m
N = 2(7) / 0.69 = 20.3
Estimated attenuation ≈ 17.5 dB

For 2000 Hz noise (λ = 0.17 m):

δ = 7 m (same)
N = 2(7) / 0.17 = 82.4
Estimated attenuation ≈ 20 dB

Higher frequencies (shorter wavelengths) produce greater barrier attenuation.