A finite difference scheme for acoustic transmission through the walls of distorted circular ducts and comparison with experiment

A numerical method is developed to find the structural response of the walls of cylindrical distorted circular ducts to internal plane acoustic travelling waves, and hence the internal/external sound transmission loss. Comparisons are made between experiment and theory for two “long-seam” air conditioning ducts and a squashed spiral-wound air conditioning duct. In general, reasonable agreement is obtained, when the accuracy of the geometrical specification of the ducts is taken into account. The generality of the computing code allows the method to be applied to cylindrical ducts of virtually any geometry where the radius of curvature and its first and second derivatives can be considered continuous around the duct perimeter. It is concluded that “mode-coupling” effects appear to offer a plausible explanation for the effect of wall distortion in lowering the duct wall transmission loss.     

Stiffness control of low frequency acoustic transmission through the walls of rectangular ducts

An investigation is reported here on the use of “stiffness control” to reduce low frequency acoustic “breakout” through the walls of rectangular air-moving ducts; in this, attempts are made to increase the fundamental transverse resonance frequency of the duct walls (by using materials with a high stiffness/mass ratio) so that the capacitive (stiffness) controlled nature of the wall impedance below this frequency may be exploited to raise the wall transmission loss and remove low frequency resonances. Some degree of success is achieved in this, and the results appear encouraging. As a necessary part of the work, the nature of the acoustic/structural wave combinations is explored in more detail than hitherto, and a simplified low frequency approximate method of determining the transmission loss of ducts is also given.     

Low frequency acoustic transmission through the walls of rectangular ducts

A simple theory is described for the transmission of low frequency sound through the walls of rectangular ducts, particularly those in air conditioning systems. The model is based on a coupled acoustic/structural wave system, and it is assumed that the duct radiates in the same way as a finite-length line source incorporating a single travelling wave. Measurements of wall transmission loss on two types of duct system are compared to theoretical predictions, and good agreement is obtained within the frequency range of validity of the theory. It is concluded that the present approach should give reliable estimates of noise transmission in practical situations.     

The effects of external lagging on low frequency sound transmission through the walls of rectangular ducts

Previous work by the author [1], on the transmission of internally propagated acoustic noise through the walls of rectangular ducts, is extended here in an investigation of the effects of external “lagging” (consisting of a layer of porous sound-absorbing material, and an impervious external covering) on the duct walls; this type of treatment is commonly applied as a noise control measure. A simple theoretical model, based, as before, on a coupled acoustic/structural wave system, is devised and shown to give reasonably accurate predictions in comparison with measurements of the wall transmission loss (though not in the case of lagging in which an external covering of very non-uniform thickness is incorporated). The conclusion is reached that external lagging used as an acoustic treatment is not, in general, particularly satisfactory.     

Higher order mode acoustic transmission through the walls of rectangular ducts

As an extension of previous work on low frequency fundamental mode acoustic transmission through the walls of rectangular ducts, results are presented here on the transmission of internally propagated higher order acoustic modes through the duct walls. Subject to various assumptions, it is possible to obtain a closed form solution to the structural wave equation governing the motion of the duct's walls, and this is used to predict the response of the walls to the internal pressure field. The resultant acoustic radiation is estimated here by assuming that the duct radiates like a circular cylinder with the same surface velocity distribution. Both experimental and theoretical results are given and agreement between the two is tolerably good.     

Approximate asymptotic solutions for acoustic transmission through the walls of rectangular ducts

Approximate expressions—valid at sufficiently high frequencies—are obtained for the acoustic transmission loss of the walls of rectangular ducts. Single mode propagation inside the duct, both in the fundamental mode and in higher order modes, is considered and a multimode model is also proposed. These theories lead to very simple formulae for the transmission loss, which prove to be in tolerably good agreement with measurements.     

Sound transmission in pipes with porous walls

Pipes with porous (permeable) walls have received the attention of several authors as a noise control element in automotive intake systems; however, a closed theory of sound transmission including the effect of the coupling of the internal and external acoustic fields and the presence of mean flow does not appear to be available. The present paper proposes an integro-differential system for the propagation of plane sound waves in pipes with porous walls, and presents its general numerical solution, as well as an approximate analytical solution. The predicted effect of the coupling between the internal and external acoustic fields in a circular pipe made of reinforced woven fabric walls is shown, and the transmission loss predictions are compared with the existing experimental data in the literature.     

Enhanced sound transmission from water to air at low frequencies

Excitation of acoustic radiation into the air from a low-frequency point source under water is investigated using plane wave expansion of the source spectrum and Rayleigh reflection/transmission coefficients. Expressions are derived for the acoustic power radiated into air and water as a function of source depth and given to lowest order in the air/water density ratio. Near zero source depth, the radiation into the water is quenched by the source's acoustic image, while the power radiated into air reaches about 1% of the power that would be radiated into unbounded water.     

Sound transmission through opened windows

Two different models have been derived in order to compute sound transmission through opened windows. The first model is a hybrid model which combines modal, geometrical, wave and integral approaches. The second model is a multi-domain BEM approach which is used as a reference. Comparisons have also been made with published measurements. Numerical aspects are discussed. SEA computations are used to compute structure born transmission in order to verify the predominance of acoustical transfer through the windows.     

Sound generation and transmission in flow ducts with axial temperature gradients

This article describes a one-dimensional, linearized, analysis of fundamental mode sound generation and propagation in rigid-walled flow ducts with axial temperature variation. An acoustic wave equation, including damping effects and volume sources, is derived and its solution (in the absence of sources) by a numerical technique and an approximate analytical method is discussed. The “forced” wave equation is then solved (the existence of an oscillating solution to the “unforced” equation being assumed) for sound generation by a side-branch volume source in an infinite duct, and the results are applied to a duct of finite length. Reasonably good agreement is obtained between measurements and predictions of the sound pressure field in a flow duct, away from the source region.     

Low frequency sound transmision through the walls of rectangular ducts: Further comments

The absence of an established criterion for housing site design against railway noise presents problems for environmental health officers who are consulted at the planning stage of housing sites. A guidance standard is suggested and experiences of a recent housing development are described.     

Sound transmission of cavity walls due to structure borne transmission via point and line connections

The author has published equations for predicting the air borne sound transmission of double leaf cavity walls due to the structure borne sound transmission across the air cavity via (possibly resilient) line connections, but has never published the full derivation of these equations. The author also derived equations for the case when the connections are rigid point connections but has never used them or published them or their derivations. This paper will present the full derivation of the author's theory of the air borne sound transmission of double leaf cavity walls due to the structure borne sound transmission across the air cavity via point or line connections which are modeled as four pole networks. The theoretical results will be compared with experimental results on wooden stud cavity walls from the National Research Council of Canada because the screw spacing is given for these results. This enables connections via studs and screws to be modeled as point connections and avoids the need to make any assumptions about the compliance of the equivalent point or line connections.     

Sound transmission through double partitions with cavity absorption

The sound transmission through double partitions with cavity absorption is discussed. A simple model is considered, consisting of two parallel thin elastic plates containing sound-absorbing material in the cavity between them. An expression for the transmission loss is obtained and calculations carried out for representative examples are compared with existing experimental values. The agreement in all cases is good.     

Investigation into higher-order mode propagation through orifice plates in circular ducts

Most established techniques for analyzing sound transmission in ducts containing orifices plates are only applicable for plane wave propagation. Once the wavelength of the sound approaches the cross section of the duct, higher order mode propagation in the system must be considered in the analysis. This is a numerically intensive activity if fully coupled calculations of the higher order modes are undertaken. This investigation estimates the acoustic fields in a duct with a simple orifice plate installed using an uncoupled model to estimate the higher order mode contribution. The uncoupled model is then used as the basis for a hybrid decomposition approach to estimate the sound field in the regions before and after the orifice plate installed in a circular duct. This approach is applied to a duct, excited by a point source over a wide frequency range, containing a single orifice plate installed a distance inside the duct. Different orifice plates with one, two and multiple openings are investigated. Of particular interest is the location of the point source relative to the duct axis. If the source is located concentric to the duct axis then, without any orifice plate present, only axially symmetric higher order modes may be excited in the duct. Thus, the investigation considers the point source located in the concentric position and in eccentric positions to vary the contribution from the different types of higher order mode. Estimates of the acoustic fields in the duct obtained using the hybrid decomposition approach are compared with measured data and the applicability of using an uncoupled estimate for the acoustic fields is commented on.     

Heterodyne spectroscopy at very low frequencies

We have studied the spectrum of light scattered by capillary waves, thermally excited at the free surface of highly viscous liquids, by heterodyne spectroscopy techniques. We were able to measure spectral widths down to 0.2 Hz.