A Statistically Based Method for Assessing Calibration Curves for the Frequency Dependence of Glycerol's Ultrasonic Attenuation

Ultrasound is an important tool for many industrial applications, including in-line real-time process monitoring. However, the use of a metrological approach is not as widespread as it could be, for instance, for ultrasonic attenuation measurements. The main goal of this paper is to present a complete uncertainty budget for individual data points and the regression curve for the calibration of glycerol's ultrasonic attenuation as a function of frequency in the range of 1.0–5.0 MHz. Experimental data were acquired using a pulsed stepped-sine 20-cycle burst ultrasonic scheme. Attenuation was calculated using both theoretical and experimental approaches to validate the experimental setup and method. Experimental and theoretical attenuation variances are statistically homogeneous across all frequencies (Fisher test; p = 0.95), and attenuation pairs of results are statistically equivalent across all frequencies ( t -Student test; p = 0.95). Theoretical and experimental attenuation coefficients were assessed using a regression curve of corrected attenuation results at 20 °C. For data from 1.0 to 5.0 MHz, the theoretical slope is 0.2847 dB cm −1 MHz −2 , and the experimental slope is 0.2582 dB cm −1 MHz −2 . Combining both slopes for a limited frequency range (1.0–3.5 MHz), the attenuation coefficient for pure glycerol at 20 °C is 0.249 dB⋅cm −1 ⋅MHz −2 with expanded uncertainty of 0.016 dB⋅cm −1 ⋅MHz −2 ( p = 0.95). The presented method can be used in other chemometric approaches to assess, for instance, biofuel quality and purity.