Page 29 - Fall2020

Figure 2. Middle ear sound transmission in two high- frequency-hearing animals. A: comparison in gerbil of middle ear transmission, represented by stapes velocity (VST; solid line) and cochlear pressure (PC; dotted line) plotted versus hearing sensitivity, represented by an audiogram (dashed line). The audiogram has a narrower frequency bandwidth than VST or PC, suggesting that hearing is limited by the cochlea rather than by the middle ear. Figure adapted from Ruggero and Temchin, 2002. B: middle ear transmission magnitudes in an individual mouse ear over the 2- to 60-kHz range, represented as ratios of ossicular chain velocity and ear canal pressure. The various lines represent different locations measured on the ossicles, as indicated by dots with matching colors (inset). Figure adapted from Dong et al., 2013, with permission.
The middle ear transmits sound over a broad frequency range that varies by species. Generally, animals with smaller heads can hear higher frequencies because only the shorter wavelengths of these sounds can vary enough between their two ears to assist in sound localization, a significant advantage for predator avoidance. It is now gen- erally accepted that the bandwidth of hearing is limited by
the capabilities of the cochlea, not by those of the middle ear (Figure 2; Ruggero and Temchin, 2002).
Remarkably, sound transmission through the middle ear varies relatively smoothly with frequency across a wide fre- quency range. This appears to hold true for large mammals like elephants, all the way down to small mammals like gerbils (Figure 2A) or mice (Figure 2B) that can hear up to 85 kHz. This smooth wideband transmission through the middle ear involves a significant amount of delay.
Middle Ear Modeling and Delay
Sound takes a surprisingly long time to pass through the middle ear. For humans and domestic cats, the delay is approximately 100 μs, which corresponds to the amount of time needed for sound to travel through a 3.4-cm-long air- filled tube (Puria and Allen, 1998). This delay is remarkable considering that the largest structural dimension in the middle ear, the eardrum diameter, is significantly smaller than this hypothetical tube length. Models composed of a few coupled second-order resonances representing dif- ferent parts of the middle ear were not able to capture the observed delays and could not realistically represent the full frequency bandwidth of the middle ear.
This led to the idea of representing the eardrum and ossicles as two coupled transmission lines (Puria and Allen, 1998). Inherent in the behavior of a transmission line is a propaga- tion delay through the system, with little loss. Incorporating transmission lines into circuit models led to a better descrip- tion of measurements at both low and high frequencies and also captured the observed delays in the middle ear.
That there is significant delay as a surface wave travels from the eardrum periphery toward the attached mal- leus handle is supported by several direct measurements in gerbils (de La Rochefoucauld et al., 2010), humans (Cheng et al., 2013), and, more recently, mice (Dong et al., 2013). Waves traveling around the eardrum circumference have also been observed (Cheng et al., 2013). Although it remains unclear what functional role, if any, middle ear delay plays in hearing, a potential scenario is described in A Possible Connection Between Hearing and Seeing.
An explanation of transmission delay through the eardrum first requires delving into its material composition. The mam- malian eardrum is unique among vertebrates in having a composite structure with distinct radial and circumferential
Fall 2020 • Acoustics Today 29