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Development of an experimental set-up to measure sound absorption coefficients of porous materials

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Abstract

This paper discusses the practical aspects of data acquisition and signal processing techniques involved while developing an impedance tube. Microphones, data acquisition systems, set of speakers were carefully selected, calibrated, and assembled as one unit. The raw time signal is acquired through a Virtual Instrument (VI) developed in LabVIEW, and the mathematical equations involved in the process are implemented in MATLAB R 2017a. Important considerations involved in these processes have been thoroughly discussed in the paper. The final results contained outliers that were removed by the application of digital filters. The results obtained from the application of different types of digital filters are shown, discussed, and the best combination of filters has been selected. This combination results in a robust and efficient method with an improved low-frequency response (< 250 Hz) which, in a standard commercial impedance tube, was achieved by altering the microphone spacing. The validation was performed by conducting experiments on a blank tube, melamine foam, glass wool, and comparison were made with the result obtained on the set-up of a leading manufacturer, and with the ones reported in works of literature. They show a good match between them which completes the validation.

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Abbreviations

D:

The diameter of the tube

c:

Speed of sound

fu :

Upper working frequency limit

S:

Spacing between the microphones

\( {\text{G}}_{12} \) :

Cross power spectrum

\( {\text{G}}_{11} \) :

Auto power spectrum

s:

Spacing between the microphones

k:

Complex wave number

\( {\text{k}}'' \) :

Attenuation constant

\( \alpha \) :

Sound absorption coefficient

K(s):

Window length in a Hampel filter

B&K:

Brüel & Kjær

\( {\text{H}}^{\text{I}} \) :

The calibration transfer function of the tubes in standard configuration

\( {\text{H}}^{\text{II}} \) :

Calibration factor in swapped configuration

\( {\text{H}}_{\text{c}} \) :

Calibration factor

\( {\text{H}}' \) :

The transfer function of the absorptive sample

H:

Corrected transfer function

\( {\text{R}} \) :

Complex reflection coefficient

l :

Distance between the second microphone and sample

\( {\text{k}}' \) :

The real component of wavenumber

f:

Frequency

Sigma (s):

Filter factor in a Hampel filter

SAC:

Sound absorption coefficient

DAQ:

Data acquisition system

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Authors and Affiliations

  1. Industrial Tribology, Machine Dynamics and Maintenance Engineering Centre (ITMMEC), Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

    Manish Raj, Shahab Fatima & Naresh Tandon

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  1. Manish Raj
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  2. Shahab Fatima
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  3. Naresh Tandon
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Correspondence to Shahab Fatima.

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Raj, M., Fatima, S. & Tandon, N. Development of an experimental set-up to measure sound absorption coefficients of porous materials. Sādhanā 45, 138 (2020). https://doi.org/10.1007/s12046-020-01367-5

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