Amplitudes of odd order distortion products (DPs) that are detected in animal ear canals have been used to probe cochlear health, to search for cochlear amplification, and to measure aspects of cochlear mechanical frequency response. Like the DP amplitude, DP phase is also an important measure of the cochlear mechanical response. Reported here are measurements of DP phase in the ear canal of the cat. The phase data show frequency-dependent time delays. One of these delays is a function of f2, the frequency of the higher-frequency primary. Hence the DP phase φd is of the form φd0dτ, where ωd is the DP angular frequency and τ is a fixed time delay. Our results show that φd is independent of input level a2 as long as the ratio a2/a1⩽2, where a2 and a1 are the amplitudes of the input tones. As a2/a1 becomes greater than two, the fixed time delays increase for DPs whose frequencies are less than the frequencies of the input tones. When both levels are varied together the delay increases as the levels decrease. There can be phase changes as large as π associated with deep nulls in the DP magnitude for the two lower-frequency DPs. Features of the nulls may be modeled assuming that there is partial reflection of the DP wave from the DP place. The assumption of energy reemitted from the DP place also explains amplitude-ratio-dependent time delays and 2π level-dependent bifurcations in phase. The DP phase shows different dependencies for f2<1 kHz compared to f2>2 kHz.

1.
Allen
,
J. B.
(1980). “
Cochlear micromechanics—A physical model of transduction
,”
J. Acoust. Soc. Am.
68
,
1660
1670
.
2.
Allen
,
J. B.
(1983). “
Magnitude and phase frequency response to single tones in the auditory nerve
,”
J. Acoust. Soc. Am.
73
,
2071
2092
.
3.
Allen, J. B. (1986). “Measurement of eardrum acoustic impedance,” in Peripheral Auditory Mechanisms, edited by J. B. Allen, J. L. Hall, A. Hubbard, S. T. Neely, and A. Tubis (Springer-Verlag, New York), pp. 44–51.
4.
Allen
,
J. B.
, and
Fahey
,
P. F.
(1992). “
Using acoustic distortion products to measure the cochlear amplifier gain on the basilar membrane
,”
J. Acoust. Soc. Am.
92
,
178
188
.
5.
Allen
,
J. B.
, and
Fahey
,
P. F.
(1993). “
A second cochlear frequency map that correlates distortion product and neural tuning measurements
,”
J. Acoust. Soc. Am.
94
,
809
817
.
6.
Allen, J. B., Shaw, J., and Kimberley, B. P. (1995). “Characterization of the nonlinear ear canal impedance at low sound levels,” Abstracts of the Eighteenth Midwinter Research Meeting, Association for Research in Otolaryngology, edited by G. R. Popelka (unpublished).
7.
Bode, H. W. (1945). Network Analysis and Feedback Amplifier Design (Van Nostrand, New York).
8.
Born, M., and Wolf, E. (1975). Principles of Optics (Pergamon, New York), 5th ed.
9.
Bowman
,
D. M.
,
Brown
,
D. K.
,
Eggermont
,
J. J.
, and
Kimberley
,
B. P.
(1997). “
The effect of sound intensity in f1-sweep and f2-sweep distortion product otoacoustic emissions phase delay estimates in human adults
,”
J. Acoust. Soc. Am.
101
,
1550
1559
.
10.
Brown, A. M., and Gaskill, S. A. (1990). “Can basilar membrane tuning be inferred from distortion measurement?,” in The Mechanics and Biophysics of Hearing, edited by P. Dallos, C. D. Geisler, J. W. Matthews, M. A. Ruggero, and C. R. Steele (Springer-Verlag, New York), pp. 164–169.
11.
Brown
,
A. M.
,
Gaskill
,
S. A.
,
Carlyon
,
R. P.
, and
Williams
,
D. M.
(1993a). “
Acoustic distortion as a measure of frequency selectivity: Relation to psychophyical equivalent rectangular bandwidth
,”
J. Acoust. Soc. Am.
93
,
3291
3297
.
12.
Brown
,
A. M.
,
Gaskill
,
S. A.
, and
Williams
,
D. M.
(1992). “
Mechanical filtering of sound in the inner ear
,”
Proc. R. Soc. London, Ser. B
250
,
29
34
.
13.
Brown
,
A. M.
,
Harris
,
F. P.
, and
Beveridge
,
H.
(1996). “
Two sources of acoustic distortion products from the human cochlea
,”
J. Acoust. Soc. Am.
100
,
3260
3267
.
14.
Brown
,
A. M.
,
Williams
,
D. M.
, and
Gaskill
,
S. A.
(1993b). “
The effect of aspirin on cochlear mechanical tuning
,”
J. Acoust. Soc. Am.
93
,
3298
3307
.
15.
Fahey
,
P. F.
, and
Allen
,
J. B.
(1985). “
Nonlinear phenomena as observed in the ear canal and at the auditory nerve
,”
J. Acoust. Soc. Am.
77
,
599
612
.
16.
Fahey, P. F., and Allen, J. B. (1986). “Characterization of cubic intermodulation distortion products in the cat external auditory meatus,” in Peripheral Auditory Mechanisms, edited by J. B. Allen, J. L. Hall, A. Hubbard, S. T. Neely, and A. Tubis (Springer-Verlag, New York), pp. 314–321.
17.
Fahey, P. F., and Allen, J. B. (1988). “Power law features of acoustic distortion product emissions,” in Basic Issues in Hearing, edited by H. Duifhuis, J. W. Horst, and H. P. Wit (Academic, London), pp. 124–131.
18.
He
,
N.
, and
Schmiedt
,
R. A.
(1993). “
Fine structure of 2 f1−f2 distortion product emissions: changes with primary level
,”
J. Acoust. Soc. Am.
94
,
2659
2669
.
19.
He, N., and Schmiedt, R. A. (1996). “On the generation site of the fine structure of 2 f1−f2 acoustic distortion product in the human ear,” Abstracts of the Nineteenth Midwinter Research Meeting, Association for Research in Otolaryngology, edited by G. R. Popelka (Association for Research in Otolaryngology, Des Moines, IA).
20.
Hubbard
,
A.
(1993). “
A traveling-wave amplifier model of the cochlea
,”
Science
259
,
68
71
.
21.
Kim
,
D. O.
, and
Molnar
,
C. E.
(1979). “
A population study of cochlear nerve fibers: comparison of spatial distributions of average-rate and phase-locking measures of responses to single tone
,”
J. Neurophysiol.
42
,
16
30
.
22.
Kimberley
,
B. P.
,
Brown
,
D. K.
, and
Eggermont
,
J. J.
(1993). “
Measuring human cochlear traveling wave delay using distortion product emission phase responses
,”
J. Acoust. Soc. Am.
94
,
1343
1350
.
23.
Matthews, J. W., and Molnar, C. E. (1986). “Modeling of intracochlear and ear canal distortion product 2 f1−f2,” in Peripheral Auditory Mechanisms, edited by J. B. Allen, J. L. Hall, A. Hubbard, S. T. Neely, and A. Tubis (Springer-Verlag, New York), pp. 258–265.
24.
O Mahoney
,
C. F.
, and
Kemp
,
D. T.
(1995). “
Distortion product otoacoustic emission delay measurement in human ears
,”
J. Acoust. Soc. Am.
97
,
3721
3735
.
25.
Piskorski, P., Long, G. R., Talmadge, C. L., and Tubis, A. (1995). “Origin of the fine structure of the distortion product emissions in the human ear,” Abstracts of the Eighteenth Midwinter Research Meeting, Association for Research in Otolaryngology, edited by G. R. Popelka (Association for Research in Otolaryngology, Des Moines, IA).
26.
Rhode
,
W. S.
(1980). “
Cochlear partition vibration-recent views
,”
J. Acoust. Soc. Am.
67
,
1696
1703
.
27.
Rosowski, J. J., Carney, L. H., Lynch, T. J. III, and Peake, W. T. (1986). “The effectiveness of external and middle ears in coupling acoustic power into the cochlea,” in Peripheral Auditory Mechanisms, edited by J. B. Allen, J. L. Hall, A. Hubbard, S. T. Neely, and A. Tubis (Springer-Verlag, New York), pp. 3–12.
28.
Ruggero
,
M. A.
, and
Rich
,
N. C.
(1991). “
Application of a commercially-manufactured Doppler-shift laser velocimeter to the measurement of basilar-membrane vibration
,”
Hearing Res.
51
,
215
230
.
29.
Ruggero
,
M. A.
,
Robles
,
L.
, and
Rich
,
N. C.
(1992). “
Two-tone suppression in the basilar membrane of the cochlea: mechanical basis of auditory-nerve rate suppression
,”
J. Neurophysiol.
68
,
1087
1099
.
30.
Schroeder
,
M. R.
(1969). “
Relation between critical bands in hearing and the phase characteristics of the cubic difference tones
,”
J. Acoust. Soc. Am.
46
,
1488
1492
.
31.
Stover
,
L.
,
Neely
,
S. T.
, and
Gorga
,
M. P.
(1996). “
Latency and multiple sources of distortion product otoacoustic emissions
,”
J. Acoust. Soc. Am.
99
,
1016
1024
.
32.
Sun
,
X.-M.
,
Schmiedt
,
R. A.
,
He
,
N.
, and
Lam
,
C. F.
(1994). “
Modeling the fine structure of the 2f1−f2 acoustic distortion product. I. Model development
,”
J. Acoust. Soc. Am.
96
,
2166
2174
.
33.
Talmadge, C., Piskorski, P., Tubis, A., and Long, G. (1996). “Evidence for multiple spatial origins of the fine structure of distortion product otoacoustic emissions in humans, and its implications experimental and modeling results,” Abstracts of the Nineteenth Midwinter Research Meeting, Association for Research in Otolaryngology, edited by G. R. Popelka (Association for Research in Otolaryngology, Des Moines, IA).
34.
Talmadge
,
C.
,
Tubis
,
A.
,
Piskorski
,
P.
, and
Long
,
G.
(1995). “
Modeling distortion product otoacoustic emission fine structure in humans
,”
J. Acoust. Soc. Am.
97
,
3413
.
35.
Voss
,
S. E.
, and
Allen
,
J. B.
(1994). “
Measurement of acoustic impedance and reflectance in the human ear canal
,”
J. Acoust. Soc. Am.
95
,
372
384
.
36.
Whitehead
,
M. L.
,
Stagner
,
B. B.
,
Lonsbury-Martin
,
B. L.
, and
Martin
,
G. K.
(1994). “
Measurement of otoacoustic emissions for hearing assessment
,”
IEEE Eng. Med. Biol. Mag.
13
,
210
226
.
37.
Whitehead
,
M. L.
,
Stagner
,
B. B.
,
Lonsbury-Martin
,
B. L.
, and
Martin
,
G. K.
(1995). “
Dependence of distortion-product otoacoustic emissions on primary levels in normal and impaired ears. II. Asymmetry in L1 and L2 space
,”
J. Acoust. Soc. Am.
97
,
2359
2377
.
38.
Whitehead
,
M. L.
,
Stagner
,
B. B.
,
Martin
,
G. K.
, and
Lonsbury-Martin
,
B. L.
(1996). “
Visualization of the onset of distortion- product otoacoustic emissions, and measurement of their latency
,”
J. Acoust. Soc. Am.
100
,
1663
1679
.
39.
Zweig
,
G.
, and
Shera
,
C. A.
(1995). “
The origin of periodicity in the spectrum of evoked otoacoustic emissions
,”
J. Acoust. Soc. Am.
98
,
2018
2047
.
40.
Zwicker, E. (1981). “Cubic difference tone level and phase dependence on frequency and level of primaries,” Psychological, Physiological and Behavioral Studies in Hearing, edited by G. van den Brink and F. A. Bilsen (Delft U.P., Delft, The Netherlands), pp. 268–273.
41.
Zwicker
,
E.
, and
Harris
,
F. P.
(1990). “
Psychoacoustical and ear canal cancellation of (2f1−f2)-distortion products
,”
J. Acoust. Soc. Am.
87
,
2583
2591
.
This content is only available via PDF.
You do not currently have access to this content.