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Anatomy and physics of the exceptional sensitivity of dolphin hearing (Odontoceti: Cetacea)

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Abstract

During the past 50 years, the high acoustic sensitivity and the echolocation behavior of dolphins and other small odontocetes have been studied thoroughly. However, understanding has been scarce as to how the dolphin cochlea is stimulated by high frequency echoes, and likewise regarding the ear mechanics affecting dolphin audiograms. The characteristic impedance of mammalian soft tissues is similar to that of water, and thus no radical refractions of sound, nor reflections of sound, can be expected at the water/soft tissue interfaces. Consequently, a sound-collecting terrestrial pinna and an outer ear canal serve little purpose in underwater hearing. Additionally, compared to terrestrial mammals whose middle ear performs an impedance match from air to the cochlea, the impedance match performed by the odontocete middle ear needs to be reversed to perform an opposite match from water to the cochlea. In this paper, we discuss anatomical adaptations of dolphins: a lower jaw collecting sound, thus replacing the terrestrial outer ear pinna, and a thin and large tympanic bone plate replacing the tympanic membrane of terrestrial mammals. The paper describes the lower jaw anatomy and hypothetical middle ear mechanisms explaining both the high sensitivity and the converted acoustic impedance match.

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Acknowledgments

We thank the associate editor Dr. Peter Narins, and two anonymous reviewers for their constructive criticism and helpful suggestions for improving earlier versions of this manuscript. This work was supported by the Academy of Finland (SN), and the Finnish Society of Sciences and Letters (TR).

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  1. Department of Biosciences, University of Helsinki, Viikinkaari 1, P.O. Box 65, 00014, Helsinki, Finland

    Simo Hemilä, Sirpa Nummela & Tom Reuter

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  1. Simo Hemilä
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Correspondence to Sirpa Nummela.

Appendices

Appendix 1: Definitions and characteristic values

Sound velocityc is 343 m/s in air at 20°C and increases slightly with temperature. In water at 13°C sound velocity is 1,500 m/s and increases slightly with temperature, pressure and salinity (Urick 1975). The wave length of sound is λ = c/f:

 

f (frequency)

100 Hz

1 kHz

10 kHz

100 kHz

λ in air

3.4 m

0.34 m

3.4 cm

0.34 cm

λ in water

15 m

1.5 m

15 cm

1.5 cm

Characteristic impedance Zc is a property of the medium. When a plane wave travels in a medium, e.g., in air or in water, at each point the acoustic pressure p is proportional to the average particle velocity u, and Zc = p/u. Zc is measured in units Pa s/m. The characteristic impedance does not depend on frequency. In air at 20°C Zc is c. 408 Pa s/m, in water c. 1,500 kPa s/m.

Acoustic impedance Za is a property of a surface, usually an opening to a specific space or to a device (e.g., an input impedance of the middle ear). When a sinusoidal pressure p is applied to that surface and the rate of volume displacement of a medium is U, the acoustic impedance is Za = p/U. Za is measured in units Pa s/m3, also called MKS acoustic ohms. Za is usually strongly frequency-dependent. Elastic or inertial forces lead to a phase shift between the sine waves p and U. Therefore, the value of Za is in general a complex number.

Specific acoustic impedance Zs is also a property of an opening to a specific space. Let a sinusoidal acoustic pressure p lead to vibration of a piston of area A in a tube or in an opening to a device. When the velocity of that piston is u, the rate of volume displacement is U = Au. Then the specific acoustic impedance is Zs = p/u = AZa, measured in Pa s/m. Here it is assumed that the specific acoustic impedance Zco of the mammalian cochlea (the input impedance) is roughly 150 kPa s/m.

Mismatch of characteristic impedances leads to partial reflection of sound in the interface of two media. When sound arrives perpendicularly from medium 1 (characteristic impedance Zc1) to the interface of medium 2 (characteristic impedance Zc2), the fraction of power transmitted to medium 2 is T = 4 Zc2/Zc1/(1 + Zc2/Zc1)2. From air to water the mismatch ratio Zc2/Zc1 is 3,700. The fractions transmitted (T) are as follows:

 

Zc2/Zc1

1

2 or 0.5

10 or 0.1

100 or 0.01

1000 or 0.001

3700

T (%)

100

89

33

3.9

0.4

0.11

T (dB)

0

−0.5

−5

−14

−24

−30

Assuming that the specific acoustic impedance of the cochlea is 150 kPa s/m, the mismatch ratio from air to the cochlea is 370 corresponding to T = 1.1% (−20 dB), and the mismatch ratio from water to the cochlea is 0.1 corresponding to T = 33% (−5 dB).

Appendix 2: The role of the surrounding medium for inertial effects

The role of the surrounding medium for the effect of middle ear mass can be illustrated by a comparison between two mammals which have fairly similar audiograms but live in different environments (media). The largest delphinid, the killer whale, and the mouse have similar audiograms with a steady threshold rise from about 20 to 100 kHz (Fig. 7). In relation to the mouse audiogram, the killer whale curve is slightly displaced toward higher frequencies, despite the fact that the vibrating bone structures of the whale are thousands of times heavier. However, the similar high frequency hearing limits are in full agreement with the mass inertia hypothesis, the reason being the 3,700 times higher characteristic impedance of water.

To illustrate this, let us reduce the middle ears of these animals to a rod-like bone (mass m) between a sound-receiving area A and the oval window, i.e., something like the columella in a bird or reptile middle ear. The sound wave (sound pressure p, particle velocity u) hits the mouse tympanic membrane (4.22 mm2) or the tympanic plate of the killer whale (1,830 mm2). Let f m be the frequency of lowest threshold, equal in these two species. In an ideal situation the cochlea absorbs all incident acoustic energy at this frequency, and the inertial force F i is compensated by an elastic force. At this frequency the pressure force acting on the mouse tympanic membrane or the tympanic plate of the whale is F = pA, and the inertial force is F i = 2πf m mu, where m in mouse (0.35 mg) stands for the mass of the ossicles and the tympanic membrane and m in whale (87 g) stands for the mass of the tympanic plate and the ossicles (Hemilä et al. 2001). As no sound reflection occurs at this optimum frequency, p/u is the characteristic impedance of the medium (Z) and the force ratio is F i/F = 2πf m m/AZ. The ratio of masses is 250,000, but the ratio of the products AZ is even larger, 1,600,000. Hence, in relation to the pressure force the inertial force in the killer whale may be smaller than in mouse. This rough estimation demonstrates that high frequency hearing is possible in water, although the vibrating structures are heavy.

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Hemilä, S., Nummela, S. & Reuter, T. Anatomy and physics of the exceptional sensitivity of dolphin hearing (Odontoceti: Cetacea). J Comp Physiol A 196, 165–179 (2010). https://doi.org/10.1007/s00359-010-0504-x

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