Phase-pulse method for estimating the traveling time of a sound wave when measuring the speed of sound in a water medium

The article considers the issues of increasing the accuracy of sound speed measurements in water actual both for standard installations and small-sized autonomous measuring devices. The methods for estimating the sound wave propagation time when measuring the sound speed using the time-of-flight method with a variable base are discussed. The general disadvantages of these methods are shown: low noise immunity of measurements, a small number of characteristic points of signals used to estimate time intervals, and the subjectivity of their selection. A version of the phase-pulse method is proposed that allows obtaining an integral estimate of the sound wave propagation time. A theoretical justification for the applicability of the method for measuring the sound speed in water is given. The propagation time is estimated by the frequency dependence of the sound wave phase incursion, which is obtained as the difference in phase spectra (cross phase spectrum) of copies of broadband pulses spaced apart in reception time. In the absence of sound dispersion, the cross phase spectrum is a proportional frequency dependence of the phase advance of a sound wave. Approximating the cross phase spectrum with a linear regression model, the frequency dependence is transformed into a numerical parameter, equal to the travel time of a sound wave with an accuracy of 2π.
Using the cross phase spectrum allows us to exclude the subjective factor when choosing characteristic points of the signals, control the quality of the experiment, significantly increase the noise immunity of measurements, and improve the statistical characteristics of the resulting estimate. An experiment is described to test the proposed method. The obtained estimates of the speed of sound are not inferior in accuracy to empirical formulas and standardized tabular values. The obtained results will be useful in further research aimed at increasing the accuracy of sound speed measurements using the phase-pulse method to the accuracy required for reference installations.

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