Cochlear wavenumber and impedance are mechanistic variables that encode information regarding how the cochlea works - specifically wave propagation and Organ of Corti dynamics. These mechanistic variables underlie interesting features of cochlear signal processing such as its place-based wavelet analyzers, dispersivity and high-gain. Consequently, it is of interest to estimate these mechanistic variables in various species (particularly humans) and across various locations along the length of the cochlea. In this paper, we develop methods to estimate the mechanistic variables (wavenumber and impedance) from noninvasive response characteristics (such as the quality factors of psychophysical tuning curves) using an existing analytic shortwave single-partition model of the mammalian cochlea. We then apply these methods to estimate human mechanistic variables using reported values for quality factors from psychophysical tuning curves and a location-invariant ratio extrapolated from chinchilla. Our resultant estimates for human wavenumbers and impedances show that the minimum wavelength (which occurs at the peak of the traveling wave) is smaller in base than the apex. The Organ of Corti is stiffness dominated rather than mass dominated, and there is negative effective damping prior to the peak followed by positive effective damping. The effective stiffness, and positive and negative effective damping are greater in the base than the apex. The methods introduced here for estimating mechanistic variables from characteristics of invasive or noninvasive responses enable us to derive such estimates across various species and locations where the responses are describable by sharp filters. In addition to studying cochlear wave propagation and dynamics, the estimation methods developed here are also useful for auditory filter design.