# Predicted Effects of Spectral Variations in Train Noise During Pass-by

Models for predicting the effects of noise control treatments rely heavily on the knowledge of the reference noise source spectrum. In road traffic noise studies, a standardized spectrum is used widely to account for the non-linearity in the emitted acoustic spectrum [114]. So far, no similar standard exists to regulate the noise spectrum emitted by high-speed trains. Unlike noise from continuous motorway traffic, which is a relatively stationary process, the noise spectrum of a train can vary significantly during its bypass. During the pass-by of a high-speed Intercity train, the variation of the sound pressure level (SPL), in the frequency range between 500 and 5000 Hz, can be as high as 20 dB/sec [115]. However, calculations of barrier effectiveness tend to use the average spectrum for the whole by-pass. A likely drawback in adopting an average spectrum is the failure to model the distinctive time-dependent performance of noise control elements (e.g. noise barriers) during the by-pass of a train. Indeed, the engineering measure of the in situ efficiency of a railway noise barrier, the broadband insertion loss, can vary considerably during the by-pass. Subjectively, the noticeable fluctuations in the insertion loss during the train by-pass might be more significant than the average barrier performance and should be considered when the efficiency of expensive railway noise barrier schemes is assessed. This section investigates the way in which variation in the reference noise source spectrum can result in a perceivable fluctuation of the noise efficiency of some noise barrier designs.

Figures 9.40 and 9.41 show typical narrow band spectrograms measured for the passage of the Intercity 125 (diesel) and Intercity 225 (electric) trains, respectively. The distances on the vertical axes in these Figures correspond to the time-dependent separation between the fixed receiver position on the ground and the varying position of the front locomotive in the train.

The measured narrow-band spectrograms have been used to determine the 1/3-octave band reference, time-dependent noise spectra which are required to model the time-dependent insertion loss of three different barrier shapes: a plane screen, a screen with a quadrant of cavities at its upper edge (‘spiky top’) and a T-shape noise barrier. The ‘spiky top’ barrier has been designed to achieve its maximum efficiency around 1000-2000 Hz, i.e. in the part of the spectrum where the maximum noise emission occurs (see

*Figure 9.40* The spectrogram of noise emitted by a passing Intercity 125 (diesel) travelling at 184 km/h.

*Figure 9.41* The spectrogram of noise emitted by a passing Intercity 225 (electric) travelling at 176 km/h.

Figures 9.40 and 9.41). The supposed noise control configurations are shown in Figures 9.42(a)—(c). Two sources of noise are elevated 0.3 m above the ballast and their positions coincided with the areas of rail-to-wheel interactions (see Figure 9.42). The receiver is assumed to be at ground level 10 m from the barrier.

Predictions have been made using the incoherent line source boundary element model proposed by Duhamel [116]. The model requires the discretization of the surfaces in two dimensions only since it assumes that the

*Figure 9.42* Schematic representation of the terrain, train body and the noise barrier profiles assumed for calculations with the BEM model.

barrier and rhe source are infinitely long. The pseudo-3D pressure field is calculated from

where *k(v) =* □ + *iv*, *v* > 0 is the attenuation and *p _{1D}(x,y,k)* is the 2-D,

frequency-dependent acoustic field predicted, for example, using the boundary integral equation method detailed in Chapter 8 (Section 8.2.4). In ideal circumstances, a full 3-D model would be required to predict the time- dependent insertion loss of a finite noise barrier length for a moving train of finite dimensions. Practical realization of such a 3-D model is beyond the scope of many numerical methods and likely to be beyond the capability of desk top PCs for the foreseeable future.

Using the measured time-dependent spectral data and predicted values of the insertion loss, the broadband time-dependent noise barrier insertion loss is calculated using

where *L _{0}(f„,t)* is experimentally determined time-dependent, 1/3-octave railway noise spectra,

*L*-

_{B}(f„,t) = L_{0}(f„,t)*IL*and

_{r}(f„)*IL*is the predicted 1/3-octave insertion loss. The values of

_{P}(f„)*f„*are the standard 1/3-octave band frequencies defined in the range between 63 and 3150 Hz. The resulting predictions of the time-dependent insertion loss are shown in Figures 9.43(a) and (b) for the diesel and electric trains, respectively.

The noise barrier surface and the body of the train have been assumed to be rigid so that multiple reflections are included. The acoustic surface impedance of the porous ballast and the porous grassland have been modelled using a four-parameter model (see Chapter 5) and the parameter values listed in Table 3.1.

*Figure 9.43* Predicted time-dependent, broad-band insertion losses for three barrier designs: (a) Intercity 125 (diesel); (b) Intercity 225 (electric).

The results for the Intercity 125 train demonstrate that the performance of the plane screen barrier is stable throughout the entire passage of the train. The average performance of the T-shape barrier is superior to that of plane screen; however, its dependence upon the instantaneous spectrum of the emitted noise is more pronounced. Although the average performance of the ‘spiky top’ barrier is similar or lower to that of the plane screen during the by-pass, the variation in the performance of this barrier during the by-pass is considerable. With the Intercity 225 train pass-by spectral variation, the insertion loss for the plane screen is inferior, but remarkably stable in comparison with the more complex barrier shapes. The fluctuation in the insertion loss of the ‘spiky top’ barrier is between 5 and 7 dB with a maximum fluctuation around the time of the train arrival and departure. Subjectively, this level of fluctuation might be more significant than the predicted gain of between 1 and 2 dB in the average barrier performance. Such effects should be considered when the efficiency of expensive railway noise barriers is assessed.