Low frequency tonal sound

LONG RANGE OUTDOOR PROPAGATION AND INTERFERENCE OF LOW FREQUENCY TONAL SOUND

 

G.P. van den Berg Science Shop for Physics, University of Groningen Nijenborgh 4, 9747 AG Groningen, the Netherlands

ABSTRACT

50 Hz power transformers produce line spectra with sharp peaks at frequencies of multiples of 100 Hz ('tones'). Narrow band spectra have been measured of two heavy transformers (220 / 110 kV) that caused annoyance at a distance of 3.5 kilometers in predominantly flat open grassland. Measurements were made at distances of 0.2 to 4 km in different directions. 'Tone' sound levels seem to decrease with distance as expected from a point source, but with variations of 20 dB. The cause of these variations must be interference of different paths caused by ground reflection in wind, as expected for single frequencies. However, in the area of annoyance, 3 to 4 km from the source, elevated levels were found, up to 12 dB more than expected: sound levels are as high as at a distance of some hundreds of meters from the source. Spatial and temporal variations in 'tone' level indicate that interference and focussing are the cause of these variations and of the elevated levels. The interfering components must result from different propagation paths, caused by atmospheric gradients possibly related to a small river close to the propagation path.

1.INTRODUCTION

The distant sound level produced by two high voltage 50 Hz transformers has been investigated because of complaints of residents living 3.5 km from the site. Transformers produce sound predominantly at a base frequency of twice the electric alternating current and at its higher harmonics; it's spectrum there fore resembles a comb with teeth at multiples of 100 Hz. A particular feature of high power transformers is of relevance to researchers in acoustics: it's tonal components can be measured over distances of some km's, and thus help in understanding propagation in this range.
In this case the tonal components were attenuated by geometrical spreading, interference and (for the higher frequencies) absorption. At a distance of 4 km however the sound is louder than the expected level, so in some way amplified.

2. SITUATION AND MEASUREMENT TOOLS

The site of the transformers is in flat farm, mostly meadow land, with solitary farms and houses, small quiet roads, a few busy roads and a railway that just passes the site. The site itself is grass covered with some asphalted surface. Several power lines are interconnected at the site. Two large 110/220 kV transformers (9 x 7 x 4 meter) stand a few meters apart with their lenght axes coinciding in a direction approximately north-south (20° - 200°). The line connecting the site and an area to the SE at 3 to 4 km distance where elevated sound levels are found (subsequently called: High Level or HL area) is almost perpendicular (125° - 305°) to the axis line of the transformers and, for about two-thirds of it's length, parallel to and some 100 m south of a small river.
The sound power level of each transformer had been determined by an acous tic consultant by measuring sound pressure levels very close to the transformer and integrating the measured values over the surface area. Total sound power was 110 dB(A); 99 dB(A) of this in the 125 Hz octave band containing the 100 Hz fundamental frequency, and 107 dB(A) in the 250 Hz octave band contai ning the 200 and 300 Hz harmonics.
Measurements have been made on three days, as given in table 2, in different directions relative to the site of the transformers. These directions were partly forced by wind direction: the transformer noise was measurable downwind and in a cross wind, but not in upwind positions. The distance between measure ment position and site varied from 100 m to 4 km.
Measurements were made with a handheld Larson Davis 2800 sound analyser (measurement height appr. 1.2 m) with a ½" microphone and a 10 cm diameter wind screen. The analyzer was operated in FFT (Fast Fourier Transform) mode in which narrow band spectra can be measured with a line width of appr. 1 Hz, depending on instrument settings. Some recordings have been made with a Casio DAT-recorder and analysed later. The sound levels are equivalent sound levels over periods of 10 to 100 seconds. Because of wind noise and (distant) road traffic the equivalent sound level is not easily measured over prolonged periods of time. These sources cause an effective measurement threshold of 15 tot 20 dB for the lower harmonics of the transformer sound.

Table 1. Measurement position and weather conditions

datemeasurement position relative to sitewind directionwind strength 27-4-1997WEweaksunny26-9-1997W-S-SENNEmoderatepartly clouded7-12-1997E-SES-SSWmoderateclouded, 7 C7-12-1997NNES-SSWmoderateclouded, 7 C

3. MEASUREMENT RESULTS

The left graph in figure 1 shows a number of transformer 'tone' levels measured near the site ('tone' is used here to indicate a narrow peak at n.100 Hz in the line spectrum). Differences in distance, 160 to 350 m, account for a difference in level of 20 log(350/160) . 7 dB. Since tone levels in fact vary over 10 to 30 dB, it is clear that other factors are more important.
The right graph in figure 1 shows tone levels at measurement positions in the High Level area. The scatter here, up to 20 dB, is less than at positions near the site. In this area residents expressed annoyance from the transformer 'hum'. Measurements made over several days and nights in their sleeping room on the first floor 3.5 km from the site gave the following results: for the 100 Hz tone an energy weighted average of 30 dB (= 11 dBA); 200 Hz: 43 dB (= 32 dBA); 300 Hz: 22 dB (= 15 dBA). In all three cases the standard deviation was +4 / -. dB. The difference between the in- and outdoor level was smallest for the 200 Hz tone and amounted to only 1.0 dB (outside level: 44 dB +4/-. dB).
All measured Leq's of the first three harmonics have been plotted in figure 2 as a function of distance. In each graph two lines are plotted; one is a line with a slope corresponding to spherical spreading (-20.logR) connecting the highest

Figure 1a,b. Measured transformer tone levels at nearby and distant
positions: sound pressure level vs. frequency 

Figure 2. Measured levels of 100 (fig a), 200 (fig b) and 300 (fig c) Hz tones as a function of distance: sound pressure level vs. distance

points of measurement (except for the anomalous ones at distances of 3 to 4 km), the other line is 20 dB below the first. The upper lines correspond to a sound level at 1 m distance of 109 dB for the 100 Hz tone, 107 dB for the 200 Hz tone and 93 dB for the 300 Hz tone. The 100 Hz level is in agreement with the acoustic consultant's measurement, the 200 + 300 Hz level is 6 dB lower. The High Level area is about a kilometer wide and to the SE of the transformer site. According to figure 2 levels there are up to 12 . 1 dB above the plotted lines representing the attenuation caused by just spherical spreading, and therefore must be caused by an amplifying process.

4. DISCUSSION

The pattern of measurement points (figure 2) is in agreement with what can be expected of a sound wave when absorption is negligible and interference occurs. Interference takes place between a direct horizontal sound wave travel ling over the ground and a sound wave emitted in a more or less upward direc tion being refracted downward by wind. If the two waves differ a multiple of a wave length in path length the resulting sound pressure level is doubled (+ 6 dB). If the path length differs by half a wavelenght (+ a multiple of the wave length) the two sound waves cancel, causing much lower sound levels. From propagation models based on this refraction and interference [1], and on sphe rical spreading, sound levels can be calculated that closely resemble the pat tern in figure 2, although of course the measurement points are just a small sample and widely spaced in contrast to a continuous theoretical prediction.

The anomalous high levels in the HL area must be caused by a sound focus sing process. These levels were measured (in just one of the days of measure ment) in a cross wind and are therefore not a result of sound waves trapped at ground level by repeated 'bouncing' caused by downward refraction of wind. A temperature inversion, trapping sound energy in a similar way, was unlikely as it was cloudy at the time and the night before and there was a moderate wind. According to [2] levels may be lower downwind, where sound energy is absor bed by this repeated bouncing, then sideways (cross wind). This, however, does not explain a fourfold (12 dB) increase in sound energy. A possible expla nation for this amplification may be that the river cools the nearby atmosphere and thus creates a cool air 'tunnel' in which sound energy is trapped. Much more measurements will be necessary to ascertain this hypothesis and give a more detailed relation between atmospheric conditions and sound propagation.

[1] K. Attenborough, S. Taherzadeh, H.E.Bass, X. Di, R. Raspet, G.R. Becker, A. Gudesen, A. Chrestman, G.A. Daigle, A. L'Esperance, Y. Gabillet, K.E. Gilbert, Y.L. Li, M.J. White, P. Naz, J.M. Noble, H.A.J.M. van Hoof, 'Benchmark cases for outdoor sound propagation models', J. Acoust. Soc. Am., 97 (1), 173-191, (1995)

[2] D. Larom, M. Garstang, M. Lindeque, R. Raspet, M. Zunckel, Y. Hong, K. Brassel, S. O'Beirne, F. Sokolic, 'Meteorology and elephant infrasound at Etosha National Park, Namibia', J. Acoust. Soc. Am., 101 (3), 1710-1717, (1997)