A practical approach to modelling railway vehicle interior acoustics

Abstract

The aim of the current work is to propose a practical approach for modelling the interior acoustics of railway vehicles by investigating the spatial decay of sound within the vehicle and its relation to the reverberation time and absorption. Measurements are presented of the longitudinal distribution of sound level inside five railway vehicles as well as the corresponding reverberation times. Both quantities are determined using an omnidirectional sound source located near one end of the vehicle. The measured sound pressure level follows a roughly linear dependence with longitudinal distance and the rate of decay is found to follow a consistent trend over all five datasets when plotted against reverberation time. To interpret these results, three different modelling approaches are considered: ray tracing, Statistical Energy Analysis, and an analytical corridor model. Ray tracing models with a simple geometry resembling the interior of a railway carriage are used to explore the dependence of the spatial decay and reverberation time on the absorption and scattering coefficients of the surfaces. For high values of scattering coefficient, the reverberation time approaches the Sabine estimate but for low values of scattering coefficient it can be up to a factor of 2.5 greater than this estimate. This implies difficulties in deducing the average absorption coefficients from the measured reverberation times. The spatial decay rates obtained from the ray tracing model do not have the same consistent dependence on reverberation time as the measured results, although the results for low values of scattering coefficient are closer to the measured trend than those for higher values. Investigation of the Statistical Energy Analysis approach shows that it predicts a spatial decay rate that depends explicitly on length of the subsystems used in the model; consequently, the results do not converge as the model is refined. It is possible to use modified coupling loss factors based on an analytical corridor model to give a better approximation to the spatial decay. This corridor model is shown to give results that are consistent with the measurements if the average absorption is obtained from the reverberation time using a modified formula for the mean free path length, and if the cross-section area is reduced to allow for the blocking effect of the seats. This provides a practical way forward for using SEA for the interior sound in railway vehicles.