A markovian approach to the modeling of sound propagation in urban streets

Abstract

Urban streets normally contain trees mainly for their aesthetical function. However, it is also claimed that the trees may become a possible control method for noise in streets and hence contribute another step towards a sustainable environment. This paper examined the capability of an abatement scheme based upon trees in streets through a simulation model developed using the novel approach based upon Markovian techniques. The approach treats the sound propagation process as first order Markov process characterised by a matrix of transition probabilities relating to sound radiation between surfaces. The approach assumes that the facades lining the streets and the trees reflect sound diffusely. The trees are also assumed to absorb and transmit the sound. The paper begins with the development of the key element in the modelling process i.e. the transition probability matrix, source distribution, receiver functions and Markov process. The effect of the trees on the transition probability matrix is dealt with by means of the development of masking matrices for screening coefficients. The simulation of noise propagation in streets containing obstacles is first carried out and the results were then compared with the results obtained with a commercial hybrid ray tracing and image source model, RAYNOISE using the diffuse reflection option. The results showed that sound pressure level in a street containing obstacles relative to that in an empty street predicted by the Markov model was in good agreement with predictions obtained using RAYNOISE model. Within the scope and assumptions in this study, it is shown streets containing trees and absorbent building facade result in sound reductions typically less than 1.5 dB. Hence trees in streets appear to have only a slight effect on sound attenuation, and thus make no significant contribution towards producing a sustainable environment in this respect.