Helmholtz Absorber Calculator
Absorption Coefficient vs Frequency
Frequency scale: logarithmic, 20 Hz - 20 kHz
Input Parameters
Calculated Results
Perforation Ratio
0.79%
Resonance Frequency
319 Hz
Theoretical Helmholtz frequency (actual peak may differ)
Absorption at Key Frequencies
Helmholtz Absorber Calculator - Documentation
Table of Contents
1. Overview
System Configuration
[Perforated Panel] → [Air Gap] → [Porous Absorber] → [Rigid Wall]
This calculator models a perforated panel Helmholtz absorber system consisting of four components:
- Perforated panel - The front face with regularly spaced circular holes
- Air gap - The cavity behind the panel
- Porous absorber material - Fibrous or foam material for damping
- Rigid backing wall - Non-vibrating boundary condition
- Based on the Miki (1990) model for porous materials
- Normal incidence absorption coefficient calculation
- Frequency range: 20 Hz - 20,000 Hz
- Validated against published data and commercial software
2. Acoustic Theory
2.1 Helmholtz Resonator Principle
A Helmholtz resonator consists of a cavity with a narrow neck. In our system:
- Neck: The perforations in the panel (provides mass)
- Cavity: The air gap behind the panel (provides compliance)
- Damping: The porous absorber material (provides resistance)
2.2 Transfer Matrix Method
The calculator uses the transfer matrix method to analyze the multi-layer system. Each layer is characterized by its acoustic impedance and propagation properties.
2.3 Porous Material Model (Miki 1990)
The Miki model is an empirical model that improves upon the Delany-Bazley model, particularly at low frequencies. It characterizes porous materials using a single parameter: flow resistivity (σ).
- Flow resistivity: 1,000 - 50,000 Pa·s/m²
- Frequency range: 0.01 < f·ρ/σ < 1.0
- Best for fibrous materials
3. Mathematical Formulas
3.1 Basic Parameters
Where: d = hole diameter [m], s = hole spacing [m]
Where: t = panel thickness [m], 0.8d = end correction
Where: c = 343 m/s (speed of sound), D = cavity depth [m]
3.2 Impedance Calculations
Perforated Panel Impedance:
Air Cavity Impedance:
Where: k = ω/c (wave number)
3.3 Miki Model Equations
Normalized Frequency:
Tortuosity Functions:
β_∞ = 1 + 0.107 × f_n^(-0.632)
Characteristic Impedance:
Propagation Constant:
Input Impedance (Rigid Backing):
3.4 Total System
Parallel Combination:
Total Impedance:
Absorption Coefficient:
Where: z_n = Z_total/(ρc) (normalized impedance)
4. Practical Design Guide
4.1 Construction Tips
- Sealing: All edges must be airtight - air leaks destroy performance
- Support: Panel must not vibrate - use rigid frame
- Material: Don't compress porous material - changes flow resistivity
- Backing: Wall must be rigid and non-vibrating
5. References & Resources
5.1 Key References
Books
- Cox, T.J. and D'Antonio, P. (2016). Acoustic Absorbers and Diffusers: Theory, Design and Application (3rd Edition). CRC Press.
- Allard, J.F. and Atalla, N. (2009). Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials (2nd Edition). Wiley.
- Ingard, U. (2010). Notes on Sound Absorption Technology. Noise Control Foundation.
- Kuttruff, H. (2016). Room Acoustics (6th Edition). CRC Press.
Key Papers
- Miki, Y. (1990). "Acoustical properties of porous materials - Modifications of Delany-Bazley models." Journal of the Acoustical Society of Japan, 11(1), 19-24.
- Delany, M.E. and Bazley, E.N. (1970). "Acoustical properties of fibrous absorbent materials." Applied Acoustics, 3(2), 105-116.
- Maa, D.Y. (1975). "Theory and design of microperforated panel sound-absorbing constructions." Scientia Sinica, 18(1), 55-71.
- Ingard, U. (1953). "On the theory and design of acoustic resonators." The Journal of the Acoustical Society of America, 25(6), 1037-1061.
5.2 Standards
- ISO 10534-2:1998 - Determination of sound absorption coefficient and impedance in impedance tubes
- ASTM E1050-19 - Standard Test Method for Impedance and Absorption of Acoustical Materials
5.3 Software Tools
- AFMG SoundFlow - Commercial acoustic simulation
- COMSOL Multiphysics - Acoustics Module
- ZORBA - Free absorption predictor
- Porous Absorber Calculator - Online tool
6. Quick Reference
Essential Equations
Perforation Ratio: σ = (π/4) × (d/s)²
Resonance Frequency: f₀ = (c/2π) × √(σ/(t_eff × D))
Effective Thickness: t_eff = t + 0.8d
Absorption: α = 4Re(z_n)/|1 + z_n|²
| Parameter | Symbol | Unit | Typical Range |
|---|---|---|---|
| Panel thickness | t | mm | 1-50 |
| Hole diameter | d | mm | 0.5-20 |
| Hole spacing | s | mm | 5-200 |
| Air gap | D | mm | 5-200 |
| Absorber thickness | L | mm | 10-300 |
| Flow resistivity | σ | Pa·s/m² | 1,000-100,000 |
Physical Constants
- Speed of sound: c = 343 m/s (20°C)
- Air density: ρ = 1.21 kg/m³ (20°C, 1 atm)
- Characteristic impedance: ρc = 415 Pa·s/m
Quick Design Rules
- Bass control (50-200 Hz): Large cavities (50-200mm), low perforation (0.5-2%)
- Mid control (200-1000 Hz): Medium cavities (20-50mm), medium perforation (1-5%)
- High control (>1000 Hz): Small cavities (5-20mm), high perforation (5-20%)
- Cavity depth estimate: D ≈ 86/f_target [mm] (for 1% perforation)
- Material thickness: L ≈ D (same as cavity depth)
- Flow resistivity: σ ≈ 10×ρc ≈ 4,150 Pa·s/m² (starting point)
Based on Miki (1990) model with rigid backing
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