# A Semi-Empirical Model for A-Weighted Sound Levels at Long Range

Makarewicz and Kokowski [25] have suggested a simple semi-empirical form for carrying out calculations of the variation in А-weighted levels from a stationary source for ranges up to 150 m allowing for wavefront spreading and ground effect. Their result for propagation from a point source is repeated here as Equation (11.35).

If source and receiver heights are denoted by *h _{s}* and

*h*respectively, and

_{r},*r*is their horizontal separation,

where *E* is an adjustable parameter intended to include the effect of the presence of the ground on radiation of sound energy from the source (2 > *E >* 1), L_{wa} is the А-weighted sound power level of the source and *y _{g}* is an adjustable ground parameter.

The lower the impedance of the ground, the larger is the value of *y _{g}.*

Turbulence effects can be included in Equation (11.35) by usings exp (-/,) instead of *y _{g},* where

*y,*is another adjustable parameter [25]. Air absorption is included [26] by an additional attenuation given by 10 log (1 +

*yd)*where

*X*represents a temperature- and humidity-dependent equivalent absorption coefficient (= 14x10"* at 10°C and 70% RH). With these modifications, Equation (11.35) may be extended to longer ranges. These modifications have been used for the predictions compared with data in Figure 11.20(b). The value of

*E*has not been included explicitly but assumed to be incorporated in the А-weighted source power deduced from close-range data.

Assuming a linear sound speed gradient, refraction effects may be included [27] by adding a term

to Equation (11.35), where y, is intended to include effects of both turbulence and refraction. In Figure 11.21, this latter modification has been used to compare with data obtained under downward-refracting conditions at Hucknall [22]. Additional data for А-weighted levels as a function of range have been generated from corrected level difference measurements by Parkin and Scholes under low wind and isothermal conditions at a different airfield [28]. These ‘data’ and the corresponding predictions are shown in Figure 11.20(a) also. By means of Equations (11.35) and (11.33a-11.33i), differences in the measured attenuation rates at the two airfields under acoustically neutral conditions are predicted to be the result of differences in

*Figure 11.20* А-weighted sound levels during acoustically neutral conditions measured at 1.2 m above grass at Hucknall (open boxes and circles) [23] and deduced from Parkin and Scholes’ data at Hatfield (crosses) [29] compared with predictions of (a) the exponential simulation model [10] (solid and broken lines) and (b) Makarewicz et *al* model including turbulence [22] (solid and broken lines using fitted ground parameters у = 7 * I O'^{4} and 3 * 10‘^{4} and fitted turbulence parameters у, = I O'^{7} and I O'^{6} respectively.

*Figure 11.21* Data for А-weighted levels under downwind conditions (wind speed up to 6 m/s at 6.4 m), obtained with receivers 6.4 m above grassland at Hucknall [23], compared with predictions (solid line) using (11.33a-1 l.33i) augmented by the refraction term (11.36).The values of *L _{WA}* and

*y*obtained for acoustically-neutral conditions (Figure 11.20(b)) have been used and y, = - 3.25

_{g}^{x}IO~

^{5}.The broken line represents the corresponding predictions for acoustically neutral conditions. The dash-dot line is the result of the ISO octave band method (see Chapter 12).

*Figure 11.22* Data for А-weighted levels under downwind conditions (wind speed up to 6 m/s at 6.4 m),obtained with receivers 6.4 m above grassland at Hucknall [23], compared with predictions using (11.37) with *Ц _{ш} =* 164 dB,/

_{g}= 7 x I0~

^{4}and

*y*= 8 x 10‘

_{t}^{3}(solid line) or 4 x I O'

^{2}(broken line).

turbulence rather than the result of differences in ground parameters. The ISO octave band method predictions (see Chapter 12) are also in good agreement with these data while slightly underestimating the measured attenuation.

Golebiewski [29] has suggested that the effect of turbulence, and hence *y„ *depends on the sound path height. Consequently, (11.35) and (11.36) may be rewritten in the form

where *L _{EWA}, y_{g}* and

*у,*are adjustable parameters and / depends on temperature and humidity. Figure 11.22 shows that having fixed

*L*and

_{EWA}*y*at values of 164 dB and 7xl0-

_{g}^{4}, respectively, the Hucknall downwind data are bracketed by 8 x 1CH <

*y,< 4*x 10-

^{2}.