Statistical characteristics of the field of narrow-band sound source in the reverberation tank and the optimization of hydrophone sampling

When the reverberation method is used to assess the acoustic radiation properties of underwater targets, the accuracy of the narrowband measurement is affected by the spatial inhomogeneity in the sound field. This paper addresses this issue by applying the random modal principle to analyze the statistical characteristics of the sound field of a narrowband sound source in the reverberation tank. It is determined that the mean square sound pressure of the narrowband sound source field follows a gamma distribution, while the spatial average of the mean square sound pressure follows a Gaussian distribution above the Schroeder cutoff frequency. The deterministic relationship between the confidence interval of the space-averaged sound pressure level and the number of spatial samples is established using the law of large numbers and the central limit theorem. Furthermore, an optimization design for hydrophone spatial sampling is proposed based on this formula. The reverberation tank tests verified the statistical characteristics and quantitative relationship formula of the sound field of narrowband sound sources in the reverberation tank. The findings indicate that the 95% confidence interval of the space-averaged sound pressure level is below 1.0 dB. The measurement was obtained using 90 samples in a reverberation tank with dimensions of 9.0 m × 3.2 m × 1.8 m and the frequency band from 2 kHz to 12 kHz above the Schroeder cutoff frequency. The narrow-band sound field causes a space-averaged sound pressure level with a standard deviation of less than 0.5 dB. The research findings can provide theoretical support and optimization design basis for spatially sampling of hydrophones in narrowband measurement using the reverberation method.