Acoustic wave propagation through resonating devices : design of acoustic waveguide filters

Abstract

This experimental study investigates the fundamental mode of sound attenuation in a straight section of a rigid square tube fitted with periodic profiled units of various configurations. The success of this task depends to a large extent on the proper implementation of the two microphone method of measuring the Transmission Loss ( TL ) of the profiled arrangements in the experimental setup. Related errors in transfer functions used in the two microphone method of measurement are studied and its significance on the resulting data noted. The Bloch wave functions for wave propagation in periodic structures are used to identify the characteristic Resonance Scattering Stop Band ( RSB ) and the Bragg Stop Band ( BSB ). In terms of the Resonance Scattering Stop Band (RSB) it is found that the cavity resonance of the test units is more dominant than the cavity resonance effect due to the spatial separation void. On the other hand the spatial separation void provides the main effect for the Bragg reflection attenuation. (BSB) There has been few experimental work done in the past to verify the Bragg StopBand ( BSB ) attenuation though its effect has been known in the Floquet Theorem. The present study aims at experimentally measure this BSB, the RSB and the interaction of BSB and RSB. Of the ten configurations tested in the Test Section length of 140 cm there is an optimal Period Length (P1) and Period Number ( P ) for the best BSB detection. In general the cavity filling does not affect the BSB attenuation effect. For units with the least cavity resonance, detection of BSB is not affected by filling the inter-unit space with either the low or high absorptive foams but the unit height must be higher than a certain barrier height at or below which the BSB is not detected. The experimental result shows that by filling the inter-unit space with 'absorptive' foam the low frequency TL spikes can be substantially reduced. This feature may be exploited under certain circumstances to obtain a smoother low frequency TL spectra. Potential application of this BSB in duct noise control is envisaged due to its simple and straight forward implementation within the length of the duct attenuator. Although no fluid flow conditions are measured with the present setup, due to its smaller degree of discontinuity as compared to a muffler system, flow ndise generation will likely be less; and the length of the waveguide filter can attenuate higher order modes efficiently giving a better performance in term of flow noise control than a single muffler. The overall performance of this type of filter shows potential in improving noise attenuation in duct. The study concludes in suggesting the sequence of designing such periodic configuration and stating the underlying relative importance of the Resonance Scattering Stop Band (RSB ) and the Bragg Stop Band (BSB ) in this type of duct noise attenuators.