Analytical Modelling of Natural Frequency of Tympanic Membrane as the Low-Frequency Limit of Hearing

We examine the low-frequency limit of hearing of the mammalian ear through the analytical modelling of the natural frequency of the tympanic membrane. The resulting equation of the natural frequency of the modelled tympanic membrane is numerically verified against previous theoretical studies, and is statistically validated against the experimental data on the low-frequency limit of hearing. By utilizing the Wilcoxon signed-rank test; W-values of 29 (p value = 0.25014) and 23 (p value = 0.11642) are respectively obtained for the 0.2% and 0.3% prestrain (at 5% significance level for sample size of 13). We fail to reject the null hypothesis as the W-values are within the critical values of the test statistics, and therefore conclude that the tympanic membrane acts as a low-frequency limiter of acoustic stimulus. Based on our study, we can predict the low-frequency limit of hearing in mammals (e.g., for the whale as 3.6 Hz and for the zebra as 44.0 Hz).