4.1 Acoustic immittance: impedance, admittance, the probe

The middle ear, viewed acoustically, is a system that takes pressure on its outer surface (the tympanic membrane) and delivers volume velocity on its inner surface (the stapes footplate at the oval window). Driven sinusoidally at a single frequency, this system behaves as a linear two-port: each input pressure produces a proportional output flow, with the proportionality constant set by the system’s stiffness, mass, and damping. That proportionality constant — pressure per volume velocity — is the acoustic impedance of the middle ear. Its reciprocal — volume velocity per pressure — is the acoustic admittance. Tympanometry measures admittance directly.

This lesson establishes the vocabulary. The wave-equation underpinning is developed in Sound 5.4 — Specific acoustic impedance refresher →; the anatomy of why the middle ear has an impedance at all is in Hearing 3.2 — Acoustic impedance refresher →.

Pressure, volume velocity, impedance

For a plane acoustic wave the local specific acoustic impedance — pressure divided by particle velocity — is $z = p / u$ , with units of $\text{Pa} \cdot \text{s} / \text{m}$ . For a plane wave in free space $z = \rho_0 c \approx 415\ \text{Pa} \cdot \text{s} / \text{m}$ in air, the characteristic impedance of air.

The clinical quantity is not specific impedance but acoustic impedance $Z = p / U$ , where $U = u \cdot A$ is the volume velocity through a cross-section of area $A$ . Volume velocity has units of $\text{m}^3 / \text{s}$ and is the relevant flux when the acoustic system in question is enclosed (an ear canal, a middle ear, a cochlea). Acoustic impedance has units of $\text{Pa} \cdot \text{s} / \text{m}^3 = \text{N} \cdot \text{s} / \text{m}^5$ , a unit so awkward that clinicians long ago adopted the acoustic ohm: $1\ \text{acoustic ohm} = 1\ \text{Pa} \cdot \text{s} / \text{m}^3$ .

The acoustic ohm follows the electrical analogy that runs through this whole subject: pressure is voltage, volume velocity is current, impedance is V/I = Z. Stiff structures store potential energy and contribute reactance like capacitors (or, dually, like springs); massive structures store kinetic energy and contribute reactance like inductors; lossy structures dissipate energy and contribute resistance. The electrical analogy is not just heuristic — the linearised acoustic equations are isomorphic to the equations of an LC ladder network, with element values set by the geometry and material properties of the air column and tissues.

Why admittance, not impedance

Tympanometers work in admittance: $Y = 1 / Z$ , units of $\text{m}^3 / (\text{Pa} \cdot \text{s})$ , or acoustic mmho (millimho — the inverse of milliohm). Two reasons:

The probe sees parallel elements. The probe sits in the ear canal; it drives an air column that leads to the eardrum, which leads to the ossicular chain and cochlea. The ear canal and the eardrum are in parallel from the probe’s perspective: pressure delivered at the probe tip splits between compressing the ear-canal air and moving the eardrum. Parallel elements add in admittance: $Y_\text{total} = Y_\text{canal} + Y_\text{eardrum}$ . If we worked in impedance, we’d have to take reciprocals. Working in admittance makes the algebra trivially additive.
The Jerger types are admittance shapes. The classical tympanometric types (A, As, Ad, B, C — covered next lesson) are defined by features of the admittance trace as the canal pressure is swept. A type-B tympanogram (flat, no peak) means “Y is dominated by the canal air, the eardrum contributes nothing” — a single immediate diagnosis. The same trace in impedance space would be a hyperbolic spike, much harder to read.

The cross-language word immittance — coined in the 1970s — covers either impedance or admittance, leaving the choice of representation to the instrument.

What the probe measures

A clinical tympanometer probe contains three elements packed into a soft eartip that seals the ear canal:

A loudspeaker delivering a continuous probe tone, traditionally 226 Hz (a frequency at which adult middle-ear admittance is dominated by stiffness, simplifying the interpretation). High-frequency probes (678, 1000 Hz) are standard for neonates, where mass dominates the small ear.
A microphone measuring the sound pressure level in the sealed canal. As the canal pressure changes, the measured SPL changes — this is the raw signal.
A pressure pump that sweeps the static air pressure in the canal from about +200 daPa down to about −400 daPa over a few seconds (1 daPa = 10 Pa; the unit is historical, from “decapascal”).

The trick: the probe tone’s amplitude at the loudspeaker is held constant, but its measured SPL in the canal varies inversely with how much acoustic admittance is presented at the probe tip. When admittance is high (a healthy, compliant eardrum at neutral pressure), the eardrum absorbs energy and the canal SPL drops. When admittance is low (a stiff or perforated eardrum), the eardrum reflects energy and the canal SPL rises. The tympanometer converts the moment-by-moment SPL reading into a moment-by-moment admittance value, and plots it against the swept pressure.

Calibration: the ear-canal volume

The first thing a tympanometer reports, before any tympanogram interpretation, is the ear-canal volume (ECV). This is the admittance value at extreme positive or negative pressure — where the eardrum has been pushed all the way to one of its mechanical limits and contributes essentially no admittance. At that limit, the probe is “seeing” only the air column between the probe tip and the (now-locked) eardrum.

For an air column of cross-sectional area $A$ and length $L$ , the admittance at a probe frequency $\omega$ well below the column’s resonance is

$Y_\text{air} = \frac{j \omega V}{\rho_0 c^2}, \qquad V = A L,$

so $|Y_\text{air}| \propto V$ — admittance is directly proportional to the trapped volume. The 226-Hz probe and the calibration of the instrument convert this admittance directly into a volume reading in mL, with about 1.0 mmho ≡ 1 mL of air at room temperature and standard atmospheric pressure.

Typical ECVs:

Population	Normal ECV
Adult	0.65 – 1.75 mL
Child (3–10 yr)	0.4 – 1.0 mL
Infant (< 6 mo)	0.2 – 0.5 mL

Two clinical inferences come immediately from the ECV alone:

Very high ECV with a flat tympanogram (Type B) = perforated tympanic membrane or open patent tube. The probe is seeing the canal air plus the entire middle-ear cavity, which adds 2 mL of air to the reading.
Very low ECV = probe blocked against the canal wall or by cerumen.

The volume measurement is the cheap-but-powerful built-in sanity check on every tympanogram.

⏳ The history — The history of acoustic immittance measurement

The idea of measuring the middle ear’s mechanical response by a probe in the canal goes back to the 1920s — Schuster (1934) and Metz (1946) used bridge circuits to measure mechanical impedance acoustically. Otto Metz’s 1946 monograph The Acoustic Impedance Measured on Normal and Pathological Ears established that conductive, mixed, and sensorineural losses gave distinct middle-ear impedance patterns, even before any clinical instrument existed to capture them practically.

The breakthrough was technological: in the late 1950s and 1960s, transistorised electronics let the bridge circuit be packed into a hand-held probe, and the differential measurement scheme became practical with electret microphones. The Madsen Z0-61 (1961) was the first clinical impedance bridge; the Madsen 70 (1969) was the first practical clinical tympanometer.

James Jerger’s 1970 paper Clinical experience with impedance audiometry defined the five classical tympanogram types (A, As, Ad, B, C) that bear his name and remain the standard clinical taxonomy fifty years later. Jerger’s contribution was clinical rather than physical — the underlying admittance measurements had existed for decades — but his five-letter shorthand gave audiologists a reproducible language for tympanograms that made the test universally interpretable. Like Carhart’s audiogram conventions (Ch 2), Jerger’s typology persists not because it is optimal but because it is agreed: it works as a clinical shorthand precisely because every audiologist in the world uses the same letters.

The shift from impedance to admittance as the displayed quantity was driven by Margolis and Shanks in the 1980s; admittance’s parallel-additivity makes the canal-correction trivial. The 226-Hz probe tone became standard in ANSI S3.39 (1987); the high-frequency probes for infants came in with universal newborn screening in the late 1990s.

The next lesson reads tympanograms — the five Jerger types and what each tells us about middle-ear status.