Laboratory studies of near-grazing impulsive sound propagating over rough water

If part of the propagation path is over water, then an improved understanding of impulsive sound propagation over water is important for the prediction of noise from explosions and sonic booms. Sound propagation over water is relevant also to noise from aircraft with landing approaches and takeoff trajectories over the sea, ships, offshore wind turbines, and recreational vessels such as power boats and jet skis. Since the specific impedance of water is greater than that of air by four orders of magnitude, water surfaces could be considered to be acoustically hard. On the other hand, the presence of water waves is likely to modify near-grazing sound propagation compared with that over a flat acoustically hard surface. The effects will depend on the relative magnitudes of the water wave amplitudes and sound wavelengths. Studies of the effects of small scale roughness on sound propagation near to the ground surface have shown that it alters the ground effect.^1,2 Roughness elements small compared with the incident sound wavelengths may be considered to change the effective impedance of the ground.^2–5 

Several attempts to predict the acoustical effects of water waves on sound propagation above them have been made assuming that the temporal variation in wave structures during the sound propagation can be ignored. The Generalized Terrain Parabolic Equation method has been used to predict propagation of impulses over gravitational waves on the surface of shallow water.⁶ The transmission loss over an idealized water surface formed by intersecting circular segments was predicted to be substantially greater than over a smooth surface, particularly under downward refraction conditions, and it was suggested that this is the result of upward scattering. A wide-angle parabolic equation method has been used to predict sound propagation over a rough sea surface under various meteorological conditions.⁷ The sea surface roughness was taken into account through an effective impedance. In the context of predicting sonic booms, the complex excess attenuation spectrum due to a line source above a boundary consisting of intersecting parabolas, which are representative of wind-driven deep water waves, has been predicted by a boundary element method (BEM) and has been used to deduce effective impedance as a function of sea state corresponding to mean wave heights between 0.25 and $7.5m$ and for five incidence angles at each height.⁸ The resulting predictions suggest that sea surface roughness could influence sonic boom profiles and rise times to an extent comparable to turbulence and molecular relaxation effects.

Despite these predictions, there are few data concerning sound propagation over the sea.⁹ Field trials are relatively expensive and, given the impracticability of controlling the sea state, it is difficult to make systematic observations of relationships between water wave characteristics and sound propagation effects. Laboratory measurements are an attractive alternative for exploring propagation phenomena associated with water surface roughness. Clearly it is not possible to reproduce wave heights on the order of meters in laboratory experiments. On the other hand, if the statistical properties of sea wave characteristics can be reproduced at laboratory scale using smaller amplitudes and wavelengths, then a scaling can be applied to the acoustic frequencies of interest. For example, use of water wave amplitudes between 1 and $5mm$ and water wavelengths between 10 and $100mm$ in the laboratory will require use of acoustic frequencies on the order of $103–104$ times the actual frequencies of interest. However, this requires a controllable means of generating wave characteristics representative of the sea surface.

This paper reports on the results of laboratory measurements made using the acoustic impulses from an electric spark source (main acoustic energy near $15kHz$⁠), over the surface of a water-filled container mounted on a vibrating platform. The water wave amplitude was controlled through the vibration of the platform. Analysis of received acoustic waveforms reveals systematic variations with water roughness amplitude.

A $500mm×500mm×50mm$ (deep) rectangular transparent-Perspex-walled container (subsequently called a “cell”) was filled with water to a depth of $30mm$ and mounted on a platform driven vertically by an electromagnetic shaker (V300, Gearing and Watson Ltd.). The amplitude and frequency content of the excitation signal were set by a programmable waveform generator. The vertical vibrations produced parametric instability and hence excited surface disturbances of more chaotic form than traveling waves. The water wave amplitude was measured by laser beam refraction and a PIV light sheet. The platform was vibrated at $30Hz$⁠. Platform vibration amplitudes of between 1 and $3mm$ were used to generate water waves with mean trough-to-crest amplitudes (subsequently referred to as mean amplitudes) of between 3 and $7mm$⁠. Figure 1(a) shows a schematic elevation of the measurement arrangement and Fig. 1(b) shows a snapshot of the source, receiver, and water surface during one of the tests.

The spark source electrode gap was close to the water surface $(30mm)$ and the acoustic signals from electrically generated sparks were received by an $1∕8in.$ microphone at a height of $25mm$ and a horizontal distance of $300mm$ from the source. Given that the peak spark source energy is near $15kHz$ and, assuming for convenience a peak airborne source impulse energy near $15Hz$⁠, this would correspond to a “real” source being at $25m$ height and $300m$ range. The analogue microphone signals were fed to an NI data acquisition card and the resulting digitized information was captured and saved using LabView. Two different methods were used to trigger the data acquisition; synchronization with the spark ignition and a received amplitude threshold trigger. The amplitude trigger was found to give superior results and has been used for the data reported here.

Figure 2 shows 100 “free-field” acoustical pulse waveforms and their means measured at a distance of $300mm$ from the electric spark source without and with background noise originating predominantly from the electromagnetic shaker. At $300mm$⁠, the peak pulse sound pressure level (SPL) is approximately $140dB$ re $20μPa$⁠. Without the platform shaker in operation the background overall SPL in the laboratory was $48dB$⁠. When the shaker was operating the background SPL was $69dB$⁠. The pulse waveforms are more or less identical confirming the reproducibility of the waveforms and that an adequate signal-to-noise ratio was achieved when the shaker was operating.

Figure 3 shows received waveforms in the presence of a flat stationary water surface and when the cell was replaced by a smooth plastic sheet without and with vibration amplitudes of 2 and $3mm$⁠. All of these waveforms show second peaks that correspond to specular reflections.

The source and receiver were slightly closer to the plastic sheet surface than to the water surface so the specular reflections occur earlier. In comparison with waveforms obtained over the stationary water surface [Fig. 3(a)], the tails of the waveforms obtained over the “stationary” plastic sheet [Fig. 3(b)] have a slightly wider dispersion. The appearance of a third minor peak indicates an additional reflection from the bottom of the plate. Vibration of the plastic sheet [Figs. 3(c) and 3(d)] appears to have relatively little effect on the received waveforms.

Figure 4 shows acoustical waveforms received over water waves with mean amplitudes of between 0 and $7mm$⁠. Peaks in the waveforms corresponding to direct and specularly reflected arrivals may be observed. A third relatively minor peak corresponding to a reflection from the bottom of the cell appears to be slightly enhanced when the water surface is rough. Two significant features are the systematic decrease in the amplitude of the specularly reflected component (second peak) and a systematic increase of the oscillations in the “tails” of the waveforms. These features are quantified by the data in Table I.

The received pulse waveform variability has been analyzed in two intervals; between 40 and $80μs$ and between 80 and $180μs$⁠. The former interval includes the direct and reflected arrivals, whereas the second interval is assumed to capture the tails of the waveforms. The variability has been expressed in terms of the mean of the standard deviations in the waveform amplitude observed at each time interval step in the analysis. With increasing water wave amplitude, the mean standard deviation of 100 waveforms between 40 and $80μs$ is fairly constant with wave height, whereas there is a systematic increase in the mean standard deviation of the waveforms between 80 and $180μs$⁠.

Laboratory experiments using an electrical spark source have shown two systematic effects of increasing mean water wave amplitude on the acoustic waveforms during near-grazing propagation. These are a decrease in the specularly reflected component and an increase in the variability of the tails of the waveforms. Further work will investigate the feasibility of attributing effective surface impedance spectra to the rough water surfaces and the possibility that the increased variability is associated with the generation of instantaneous acoustic surface waves.

The work was supported in part by EPSRC (UK) Grant No. EP/E027121/1.