Fig. 2

Observed infrasound spectrum and distribution of its frequency ratio. a Amplitude spectra of the infrasound signals, calculated with 10-min waveforms. Gray lines show amplitude spectra provided from the data every 10 min of the 9-h subject period, and the black line is a smoothed spectrum of their average. The distinct peak is shown at \(\sim\)0.5 Hz (\(f_\text {0}\)), and some additional peaks exist at higher frequencies. The prominent peak among them is \(\sim\)2 Hz, corresponding to overtone \(f_\text {1}\) of the acoustic resonance. b Distribution of the observed frequency ratio (\(f_\text {1}/f_\text {0}\)) and theoretical relationship between the frequency ratio and frustum radius ratio. The observed frequency ratio was calculated from the average amplitude spectrum of a (Additional file 3). The PDF of the frequency ratio is shown as a histogram. The black line is a theoretical relationship between the frequency ratio (\(f_\text {1}/f_\text {0}\)) and the radius ratio of the frustum of the open and closed ends (\(a_\text {o}/a_\text {c}\)), according to Ayers et al. (1985). The main four bins of the \(f_\text {1}/f_\text {0}\) histogram correspond to \(a_\text {o}/a_\text {c}\) values of 0.35, 0.43, 0.55, and 0.72 (dots and a cross on the black line). These values suggest that the shape of the space in the conduit widens as the depth increases. The PDF values of the four bins were used as weighting coefficients for the final summation of the results