Jongens, Adrian W.D. Application of Cepstrum Techniques and Guard Tube to the Measurement of the Normal Incident Sound Power Absorption in situ. MSc Dissertation. Department of Electrical Engineering, University of Cape Town, 1993.
The work described in this thesis was directed towards studying signal processing techniques that could best be incorporated in an apparatus that was to measure the plane wave sound power absorption coefficient of road surfaces in-situ.
Road traffic noise has been identified as the greatest noise pollutant in the industrialised world with the tyre/road interaction being the major source of noise for traffic speeds in excess of 50 km/hr. Open pore bitumen asphalt material has been found to present a sound absorbing surface that is able to contribute to the mitigation of road traffic noise. This has generated research into the production of sound absorbing road surface materials which, in turn, has generated a need for an apparatus that is able to measure the sound power absorption coefficient of such materials both in the laboratory and in the field.
It was considered that the development of an easily transportable apparatus was needed which would enable a single, non-skilled operator to measure rapidly the normal incident sound power absorption coefficient, over a broad frequency band, of road surfaces, in situ. This included, for example, the measurement of the absorption coefficient of open-pore asphalt materials developed in the laboratory, the measurement of newly laid surfaces, the comparison of different experimental surfaces, as well as determining the effect of contamination, over time, of the pores of open-pore asphalt by ingress of dust.
After considering various potential signal processing methods the work described in this thesis was primarily directed towards the study and application of cepstral signal processing techniques suitable for incorporation in the development of such a system. A prototype system for use in the laboratory was developed which generated a suitable sound signal which insonified the material under investigation, separated the reflected signal from the total signal received at a single microphone position and presented a complete spectrum of the sound power absorption coefficient within a short space of time.
Specifically, the sample impulse response was extracted from the power cepstrum of the combined signal containing the direct sound and the sound reflected from the sample. The extracted impulse response was Fourier transformed to produce the reflection coefficient from which the absorption coefficient over a frequency range of 100Hz to beyond 200Hz was derived.
Laboratory measurements were conducted on several material samples with different sound absorbing properties. The results of these measurement correlated closely with theory and with measurements conducted on the same samples using a standard impedance tube method.
The work was directed at the adaption of the well-known impedance tube method to permit the measurement of the material surface under investigation without disturbance of the surface. An important consideration was that field measurements were to be obtained without the removal of core specimens or the need to drive the tube into the surface which could otherwise alter the properties of the material. Measurements conducted with an outer “Guard” tube surrounding the measuring tube indicated that such a condition could be met.
The prototype apparatus consisted of two 2 metre long concentric tubes with a loudspeaker located at one end and open at the other end for placement on the measurement surface. Sound from the loudspeaker propagated down the inner and outer tube. The purpose of the outer “guard” tube was to provide an equilibrium of sound pressure on either side of the inner tube walls at the measurement surface thereby minimising the errors that would otherwise be introduced due to sound pressure leakage between the end of the inner measuring tube and the material being measured.
Laboratory measurements performed with microphones placed within porous material placed at the end of the tubes showed there to be no significant difference in pressure amplitude and phase over the frequency range of interest. This provided confidence in the expectation that extended material surfaces could be measured with normal incident plane waves insonifying the material.
For the majority of experiments only the inner tube was used with the material to be measured being placed in a sample holder attached to the open end of the inner tube.
The results of the work conducted in this thesis showed that, of various methods studied, the cepstrum method was the most suitable for implementation in a portable, in-situ measurement system. The plane wave sound power absorption coefficient of a material could be accurately determined over a wide frequency range within a very short period of time. The measurement procedure was several orders of magnitude quicker than existing procedures. It was shown that this could be achieved automatically, with relatively small apparatus and without the need for calibration.