Chapter 2

Notes  (26 Aug 2008)

P. 13, Fig. 2.2A: The original data for this figure can be found in Shaw, E.A.G. (1974) Transformation of sound pressure level from the free field to the eardrum in the horizontal plane. J. Acoust. Soc. Am. 56, 1848-1861, rather than in the review cited in the text, which was the source of the summary figure used here.  (26 Aug 2008)

P. 14: Alternative caption to Fig. 2.3, which more explicitly explains the details of the derivation:
Fig. 2.3 The fraction of power available from the sound field that is absorbed by the middle and inner ear, in two species, according to Rosowski (1991), where the power available depends on the size of the animal's head and external ear and the direction of the sound source. The fractional power absorption was calculated from the impedance z1 looking out through the external ear from a point lateral to the tympanic membrane and the impedance z2 looking into the middle ear from the same point. The fraction of power absorbed by the middle and inner ear depends on the interaction of the resistive (real) parts (a, x) and reactive (imaginary) parts (ib, iy) of the measured impedances. Given that z1=a + ib and z2=x +iy, the fraction of available power absorbed = 4ax/((a+x)2+(b+y)2).
(12 Aug 2008)

P. 15: Signal transmission through the outer, middle and inner ears can only be properly considered if the system is treated as a transmission line. In a transmission line, each section is reversibly coupled to the adjacent sections. Depending on the relations between the impedances of the sections, each interface will transmit and reflect energy, and each section may absorb energy. Therefore the function of any one section cannot be understood in isolation, but the system needs to be considered as a whole. In view of the coupled nature of a transmission line, disrupting any one stage can affect all other stages of the system. Measuring the efficiency of transfer through any one section, or measuring its impedance, is difficult, because this necessarily involves disrupting the other stages, which affects transmission. (15 Aug 2008).

P. 17: The so-called "buckling factor", which added an extra component to the impedance transformation, based on the measurements of Khanna and Tonndorf (1972) in the cat, has not been supported by more recent measurements, and is therefore not included here. However, it should be remarked that the more recent measurements have been made in human cadavers, and there is a considerable possibility that the mechanical properties of the middle and inner ears change after death. Secondly, in the more recent measurements in human beings, detailed measurements of different parts of the tympanic membrane were not made, and so we would not expect to find such a "buckling factor". Detailed ideas of the pattern of vibration in human beings are only known from modelling (e.g. Koike et al., 2002). These support the complex vibration patterns obtained by Khanna and Tonndorf at high frequencies, but did not address the buckling issue. (15 Aug 2008).

P. 18: Specific impedances, as used here, tell us the forces required to produce a unit linear velocity in a unit cross-sectional area of the medium. I think this is an intuitively simple concept because it can be related easily to the properties of the medium in which the wave is travelling. I have used only specific impedances in this book, because I did not want to introduce further complexities by including acoustic ohms (the pressures required to produce unit volume velocity* in a medium). However, it must be admitted that acoustic ohms are more appropriate when considering an acoustic transmission line (such as the outer and middle ears). Anyone reading the literature will need to be familiar with acoustic ohms. Acoustic ohms are either MKS acoustic ohms (dimension N.sec.m-5), or c.g.s. acoustic ohms (used in the older literature) with dimension dyn.sec.cm-5.

1 c.g.s. ohm = 105 MKS ohms.
1 c.g.s. unit specific impedance (dimension dyn.sec.cm-3) = 10 MKS units specific impedance (dimension N.sec.m-3).

*volume velocity: the number of unit volumes/second of the medium that pass through the cross-section of the place of measurement (15 Aug 2008).

P. 22, Fig. 2.7: The text in the original paper defines the ratio as "Power into cochlea/power into middle ear" rather than the slightly different form stated here (Rosowski, 1991). (15 Aug 2008)

P. 22: Calculating the efficiency of power transmission through the whole system is highly dependent on knowing the value of the input impedance of the cochlea. The cochlear input impedance can be calculated either from mathematical models (as in e.g. Zwislocki, 1965) or from direct measurements of the relation between stapes displacements and intracochlear pressures (e.g. de la Rochefoucauld O, et al. 2008: J Assoc Res Otolaryngol. 9(2):161-177 in the gerbil). Generally, the cochlea is found to be purely resistive over much of the audible frequency range. The paper by de la Rochefoucauld et al. is recommended as a current assessment of the issues described in this section. (15 Aug 2008).

P. 22, Fig. 2.7: For this figure, in order to calculate the efficiency of human middle ear, Zwislocki's theoretical estimate of human cochlear impedance was used, rather than the more recent data obtained in human cadavers. Because the more recent data show 10 dB greater transmission at the high frequencies (O'Connor and Puria, 2006), the middle ear efficiency is likely to be increased at high frequencies by approximately that amount. (15 Aug 2008)


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