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Acoustic Barrier Sound Diffraction Calculator (Maekawa Model)

Acoustic noise barriers, highway sound walls, and industrial machinery enclosures reduce ambient noise transmission into community receptors by forcing sound waves to bend (diffract) over the barrier crest.

Horizontal distance between acoustic noise source and the sound wall.

Horizontal distance from sound wall to observation receiver point.

Effective vertical projection of the barrier crest breaking the direct line-of-sight between source and receiver.

Acoustic octave band center frequency being evaluated (typically 125 to 2000 Hz).

Calculated Result
15.2 dB

Diffraction Noise Reduction (IL)

Barrier Noise Reduction (IL)

15.2 dB

Diffraction Path Difference (δ)

515 mm

Fresnel Number (N)

1.5

Acoustic Shielding Verdict

EXCEPTIONAL ATTENUATION (≥ 15 dB: Substantial quiet zone created)

Evaluated Frequency

500 Hz

Calculation Breakdown

  1. Diffracted Path Geometryδ = √(d_sb² + h²) + √(d_br² + h²) - (d_sb + d_br) = 0.515 m
  2. Fresnel Diffraction Number NN = 2δ / λ = (2 × 0.515) / (0.69 m) = 1.5
  3. Maekawa Insertion Loss FormulationIL = 10 × log₁₀(3 + 20 × N) = 10 × log₁₀(3 + 20 × 1.5) = 15.2 dB

Acoustic Barrier Diffraction Profile

Interactive visualization based on your current inputs

Value
0.03.87.61115Path Diff (m × 10)Fresnel N (×10)Insertion Loss (dB)Dist Source (m)Dist Receiver (m)ParameterValue

What Is the Acoustic Barrier Sound Diffraction Calculator (Maekawa Model)?

The Acoustic Barrier Sound Diffraction Calculator determines noise attenuation achieved by solid walls, earth berms, and industrial noise barriers.

How Does the Acoustic Barrier Sound Diffraction Calculator (Maekawa Model) Work?

It computes acoustic path length difference over the barrier lip, derives the dimensionless Fresnel number N, and applies the Maekawa formula.

Acoustic Barrier Sound Diffraction Calculator (Maekawa Model) Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

N = \frac{2 \delta}{\lambda} = \frac{2 \delta \cdot f}{c}, \quad \Delta L = 10 \log_{10}(3 + 20 N) \quad [\text{dB}]

Maekawa acoustic diffraction theory relating optical path length difference to edge wave shadow attenuation.

How to Use the Acoustic Barrier Sound Diffraction Calculator (Maekawa Model)

  1. Enter distance from noise source to barrier and barrier to receiver.
  2. Specify effective height of the wall top above the direct sightline.
  3. Choose acoustic evaluation frequency in Hz.

Step-by-Step Example Calculation

Highway Noise Wall at 500 Hz

Input Values:

distanceSourceToBarrierM:10
distanceBarrierToReceiverM:15
barrierHeightAboveLineOfSightM:2.5
soundFrequencyHz:500
Worked Steps: Produces a 0.51 m path difference with Fresnel number N = 1.49, delivering 15.16 dB sound insertion loss.

Understanding Your Result

Insertion Loss (dB): Decibel reduction in sound level at the receiver.

Fresnel Number (N): Dimensionless parameter indicating diffraction severity.

Path Length Difference: Geometric detour sound must travel around the barrier top.

Factors That Affect the Result

  • Positioning the barrier closer to either the source or the receiver maximizes path difference δ and noise reduction.
  • Higher frequencies experience dramatically greater shadow attenuation.

When Should You Use This Calculator?

  • Highway sound wall design, HVAC rooftop chiller screening, electrical substation noise abatement, and factory boundary walls.

Assumptions & Limitations

  • Assumes an infinitely long straight barrier without significant end diffraction and quiet ambient wind conditions.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Based on Maekawa (1968) and FHWA Highway Noise Barrier Design Handbook.

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