Mechanisms of generation of the 2f2-f1 distortion product otoacoustic emission in humans

The 2f1-f2 distortion product otoacoustic emission (DPOAE) is considered to consist of two components in normally hearing ears, one having constant phase with changing DP frequency (wave fixed) and one having an increasing phase lag with increasing frequency (place fixed). The aim was to identify the wave-fixed and place-fixed components of both 2f1-f2 and 2f2-f1 DPs, and, in particular, to show whether a wave-fixed 2f2-f1 DP exists in normally hearing adults. DPOAE recordings were made in 20 ears of normally hearing young adults. Four frequency ratios were used and recording entailed fixed frequency-ratio sweeps. A separation into wave-fixed and place-fixed components was carried out using a time-window separation method. A method for estimating the noise floor after data processing was developed. Results confirmed the presence of wave-fixed and place-fixed components for 2f1-f2, consistent with previous studies. Both components were also present for 2f2-f1 in virtually all subjects. This latter finding conflicts with current models of DPOAE generation, and so a modified model is proposed. Unlike the 2f1-f2 emission, which has a wave-fixed component that is strongly dependent on the frequency ratio, neither component of the 2f2-f1 emission showed such a dependence. The proposed model explains these findings in terms of the overlap of the primary frequency traveling waves.     

Cortical responses to the 2f1-f2 combination tone measured indirectly using magnetoencephalography

The simultaneous presentation of two tones with frequencies f(1) and f(2) causes the perception of several combination tones in addition to the original tones. The most prominent of these are at frequencies f(2)-f(1) and 2f(1)-f(2). This study measured human physiological responses to the 2f(1)-f(2) combination tone at 500 Hz caused by tones of 750 and 1000 Hz with intensities of 65 and 55 dB SPL, respectively. Responses were measured from the cochlea using the distortion product otoacoustic emission (DPOAE), and from the auditory cortex using the 40-Hz steady-state magnetoencephalographic (MEG) response. The perceptual response was assessed by having the participant adjust a probe tone to cause maximal beating ("best-beats") with the perceived combination tone. The cortical response to the combination tone was evaluated in two ways: first by presenting a probe tone with a frequency of 460 Hz at the perceptual best-beats level, resulting in a 40-Hz response because of interaction with the combination tone at 500 Hz, and second by simultaneously presenting two f(1) and f(2) pairs that caused combination tones that would themselves beat at 40 Hz. The 2f(1)-f(2) DPOAE in the external auditory canal had a level of 2.6 (s.d. 12.1) dB SPL. The 40-Hz MEG response in the contralateral cortex had a magnitude of 0.39 (s.d. 0.1) nA m. The perceived level of the combination tone was 44.8 (s.d. 11.3) dB SPL. There were no significant correlations between these measurements. These results indicate that physiological responses to the 2f(1)-f(2) combination tone occur in the human auditory system all the way from the cochlea to the primary auditory cortex. The perceived magnitude of the combination tone is not determined by the measured physiological response at either the cochlea or the cortex.     

Evidence for the distortion product frequency place as a source of distortion product otoacoustic emission (DPOAE) fine structure in humans. II. Fine structure for different shapes of cochlear hearing loss

Distortion product otoacoustic emissions (DPOAE) were recorded from eight human subjects with mild to moderate cochlear hearing loss, using a frequency spacing of 48 primary pairs per octave and at a level L1 = L2 = 60 dBSPL and with a fixed ratio f2/f1. Subjects with different shapes of hearing thresholds were selected. They included subjects with near-normal hearing within only a limited frequency range, subjects with a notch in the audiogram, and subjects with a mild to moderate high-frequency loss. If the primaries were located in a region of normal or near-normal hearing, but DP frequencies were located in a region of raised thresholds, the distortion product 2 f1-f2 was still observable, but the DP fine structure disappeared. If the DP frequencies fell into a region of normal thresholds, fine structure was preserved as long as DPOAE were generated, even in cases of mild hearing loss in the region of the primaries. These experimental results give further strong evidence that, in addition to the initial source in the primary region, there is a second source at the characteristic place of fDP. Simulations in a nonlinear and active computer model for DPOAE generation indicate different generation mechanisms for the two components. The disappearance of DPOAE fine structure might serve as a more sensitive indicator of hearing impairment than the consideration of DP level alone.     

Ipsilateral distortion product otoacoustic emission (2f1-f2) suppression in children with sensorineural hearing loss

Distortion product otoacoustic emission (DPOAE) ipsilateral suppression has been applied to study cochlear function and maturation in laboratory animals and humans. Although DPOAE suppression appears to be sensitive to regions of specialized cochlear function and to cochlear immaturity, it is not known whether it reflects permanent cochlear damage, i.e., sensorineural hearing loss (SNHL), in a reliable and systematic manner in humans. Eight school-aged children with mild-moderate SNHL and 20 normal-hearing children served as subjects in this study. DPOAE (2f1-f2) suppression data were collected at four f2 frequencies (1500, 3000, 4000, and 6000 Hz) using moderate-level primary tones. Features of the DPOAE iso-suppression tuning curves and suppression growth were analyzed for both subject groups. Results show that DPOAE suppression tuning curves from hearing-impaired subjects can be reliably recorded. DPOAE suppression tuning curves were generally normal in appearance and shape for six out of eight hearing-impaired subjects but showed subtle abnormalities in at least one feature. There was not one single trend or pattern of abnormality that characterized all hearing-impaired subjects. The most prominent patterns of abnormality included: broadened tuning, elevated tip, and downward shift of tip frequency. The unique patterns of atypical DPOAE suppression in subjects with similar audiograms may suggest different patterns of underlying sensory cell damage. This speculation warrants further investigation.     

Modifications of a single saturating non-linearity account for post-onset changes in 2f1-f2 distortion product otoacoustic emission

2f1-f2 distortion product otoacoustic emissions (DPOAEs) were recorded from guinea pigs. DPOAEs showed complex time dependence at the onset of stimulation. The DPOAE, measured during the first 500 ms, can either decrease or increase at the onset depending on both the frequencies and levels of the primary tones. These changes are closely associated with amplitude minima (notches) of the DPOAE I/O functions. These notches are characteristic of DPOAE growth functions measured from guinea pigs for primary tones of 50-60-dB sound-pressure level (SPL). Apparent changes in the DPOAE amplitude occur because the notch shifts to higher levels of the primaries during the onset of stimulation. This shift of the notch to higher levels increases for lower f2/f1 ratios but does not exceed about 2 dB. DPOAE amplitude increases for a constant level of the primaries if the onset emission is situated at the low-level, falling slope of the notch. If the onset DPOAE is located on the high-level, rising slope of the notch, then the upward shift of the notch causes the emission either to decrease monotonically, or to decrease initially and then increase. By establishing that the 2f1-f2 onset changes reflect a shift in the growth-function notch, it is possible to predict the temporal behavior of DPOAEs in the two-dimensional space of the amplitude of the primaries and for their different frequency ratios.     

The influence of systematic primary-tone level variation L2-L1 on the acoustic distortion product emission 2f1-f2 in normal human ears

The purpose of the present study was to determine the effect of primary-tone level variation, L2--L1, on the amplitude of distortion-product otoacoustic emissions (DPOAEs). The DPOAE at the frequency 2f1--f2 (f2 greater than f1) was measured in 20 ears of ten normally hearing subjects. Acoustic distortion products were generated by primaries f1 and f2 with geometric mean frequencies of 1, 2, and 4 kHz. The f2/f1 ratios were 1.25 (1 kHz), 1.23 (2 kHz), and 1.21 (4 kHz). The primary-tone level L1 was kept constant at either 65 or 75 dB SPL while the second primary-tone level L2 was varied between 20 and 90 dB SPL in 5-dB steps. The level differences L2--L1 generating maximal DPOAE amplitudes depended on L1 and on the geometric mean frequency of f1 and f2. There were large interindividual differences. Overall, the L2--L1 evoking maximal mean DPOAE amplitudes was --10 dB for geometric mean frequencies of 1 and 2 kHz with both L1 = 65 dB SPL and L1 = 75 dB SPL. For 4 kHz, L2-L1 was --5 dB with L1 = 65 dB SPL and 0 dB with L1 = 75 dB SPL. The mean slopes of the DPOAE growth functions in the initial linearly increasing portions were steeper at higher stimulus frequencies, increasing from 0.52 at 1 kHz to 0.72 at 4 kHz for L1 = 65 dB SPL and from 0.48 at 1 kHz to 0.72 at 4 kHz for L1 = 75 dB SPL.     

Hybrid measurement of auditory steady-state responses and distortion product otoacoustic emissions using an amplitude-modulated primary tone

A maximum auditory steady-state response (ASSR) amplitude is yielded when the ASSR is elicited by an amplitude-modulated tone (f(c)) with a fixed modulation frequency (f(m) = 40 Hz), whereas the maximum distortion product otoacoustic emission (DPOAE) level is yielded when the DPOAE is elicited using a fixed frequency ratio of the primary tones (f2/f1 = 1.2). When eliciting the DPOAE and ASSR by the same tone pair, optimal stimulation is present for either DPOAE or ASSR and thus adequate simultaneous DPOAE/ASSR measurement is not possible across test frequency f2 or f(c), respectively. The purpose of the present study was to determine whether the ASSR and DPOAE can be measured simultaneously without notable restrictions using a DPOAE stimulus setting in which one primary tone is amplitude modulated. A DPOAE of frequency 2f1-f2 and ASSR of modulation frequency 41 Hz were measured in ten normal hearing subjects at a test frequency between 0.5 and 8 kHz (f2 = f(c)). The decrease in the DPOAE level and the loss in ASSR amplitude during hybrid mode stimulation amounted, on average, to only 2.60 dB [standard deviation (SD) = 1.38 dB] and 1.83 dB (SD = 2.38 dB), respectively. These findings suggest simultaneous DPOAE and ASSR measurements to be feasible across all test frequencies when using a DPOAE stimulus setting where the primary tone f2 is amplitude modulated.     

Distortion product otoacoustic emission input/output functions in normal-hearing and hearing-impaired human ears.

DPOAE input/output (I/O) functions were measured at 7f2 frequencies (1 to 8 kHz; f2/f1 = 1.22) over a range of levels (-5 to 95 dB SPL) in normal-hearing and hearing-impaired human ears. L1-L2 was level dependent in order to produce the largest 2f1-f2 responses in normal ears. System distortion was determined by collecting DP data in six different acoustic cavities. These data were used to derive a multiple linear regression model to predict system distortion levels. The model was tested on cochlear-implant users and used to estimate system distortion in all other ears. At most but not all f2's, measurements in cochlear implant ears were consistent with model predictions. At all f2 frequencies, the ears with normal auditory thresholds produced I/O functions characterized by compressive nonlinear regions at moderate levels, with more rapid growth at low and high stimulus levels. As auditory threshold increased, DPOAE threshold increased, accompanied by DPOAE amplitude reductions, notably over the range of levels where normal ears showed compression. The slope of the I/O function was steeper in impaired ears. The data from normal-hearing ears resembled direct measurements of basilar membrane displacement in lower animals. Data from ears with hearing loss showed that the compressive region was affected by cochlear damage; however, responses at high levels of stimulation resembled those observed in normal ears.     

Evidence for two discrete sources of 2f1-f2 distortion-product otoacoustic emission in rabbit: I. Differential dependence on stimulus parameters.

The results of studies of the physiological vulnerability of distortion-product otoacoustic emissions (DPOAEs) suggest that the DPOAE at 2f1-f2 in vertebrate ears is generated by more than one source. The principal aims of the present study were to provide independent evidence for the existence of more than one DPOAE source, and to determine the contributions of each to the ear-canal 2f1-f2 signal. To accomplish these aims, specific stimulus parameters were separately and systematically varied to provide detailed parametric information regarding 2f1-f2 DPOAE amplitude and phase in normal ears of awake rabbits. The findings indicate that two discrete sources, demonstrating differential dependence on stimulus parameters, dominate the generation of the 2f1-f2 DPOAE. One source of distortion is dominant above 60-70 dB SPL at moderate primary-frequency separations, and at all stimulus levels when the primary tones are closely spaced. The other source is dominant below 60-70 dB SPL at moderate primary-frequency separations, and may be dominant at all stimulus levels when the primary tones are widely separated in frequency. The results suggest that by varying stimulus parameters, it may be possible to independently study the two generator mechanisms.     

Periodogram based tests for distortion product otoacoustic emissions

Distortion product otoacoustic emissions (DPOAEs) are an important nonbehavioral measure of cochlear function, which provides a close analogue of the behavioral pure-tone audiogram. DPOAEs are sinusoidal distortion products (DPs) produced by nonlinearities in the healthy cochlea. Detection of DPs is accomplished in the Fourier domain with a periodogram based test. The test compares the power in the DP periodogram bin to a noise estimate derived from a certain number of the surrounding bins. Statistical properties of this test to date have only been examined by constructing receiver operator characteristics curves derived from DPOAE measurements in normal and hearing impaired individuals. In this paper the null distribution of this order-statistic based test is explicitly derived, and via simulations intended to mimic the nonwhite features of real-ear noise measurements, the power of the test is demonstrated. These simulations demonstrate that a local F test is more powerful than this DPOAE test, with critical values that are easier to calculate. Although the power of both tests increase with an increasing number of bins, the improvement is negligible at around four bins. Since the power of both tests decrease at lower DP frequencies, it is not recommended to use a large number of bins.     

Influence of primary frequencies ratio on distortion product otoacoustic emissions amplitude. I. Intersubject variability and consequences on the DPOAE-gram

Distortion product otoacoustic emissions (DPOAEs) are used widely in humans to assess cochlear function. The standard procedure consists of recording the 2f1-f2 DPOAE amplitude as a function of the f2 frequency, using a fixed f2/f1 ratio (DPOAE-gram), close to 1.20. DPOAE amplitude, as recorded in the DPOAE-gram, shows a wide range of values in normal-hearing subjects, which can impair the predictive value of the DPOAE-gram for hearing thresholds. This study is aimed at comparing intersubject variability in 2f1-f2 DPOAE amplitude according to three paradigms: a fixed f2/f1 ratio, such as the DPOAE-gram, a variable ratio DPOAE-gram (f2/f1 adapted to frequency) and an "optimum" DPOAE-gram, where the f2/f1 is adapted both to subject and frequency. The 2f1-f2 DPOAE amplitude has been investigated on 18 normally hearing subjects at ten different f2 frequencies (from 0.75 to 6 kHz), using an f2 fixed, f1 sweep paradigm, and allowed to define, for each frequency, the f2/f1 ratio giving the greatest 2f1-f2 DPOAE amplitude (or optimum ratio). Results showed a large intersubject variability of the optimum ratio, especially at frequencies below 1.5 kHz, and a significant decrease of the optimum ratio with frequency. The optimum DPOAE-gram was underestimated by up to 5.8 dB on average (up to 14.9 dB for an individual subject) by the fixed ratio DPOAE-gram, and by up to 3 dB on average (up to 10.6 dB for an individual subject) by the variable ratio DPOAE-gram. Intersubject variability was slightly but significantly reduced in the optimum DPOAE-gram versus the fixed-ratio DPOAE-gram. Lastly, correlations between tone-burst evoked otoacoustic emission (TBOAE) amplitudes and maximum DPOAE amplitudes were significantly greater than correlations between TBOAE amplitudes and fixed-ratio DPOAE amplitudes.     

Evidence for the distortion product frequency place as a source of distortion product otoacoustic emission (DPOAE) fine structure in humans. I. Fine structure and higher-order DPOAE as a function of the frequency ratio f2/f1

Critical experiments were performed in order to validate the two-source hypothesis of distortion product otoacoustic emissions (DPOAE) generation. Measurements of the spectral fine structure of DPOAE in response to stimulation with two sinusoids have been performed with normal-hearing subjects. The dependence of fine-structure patterns on the frequency ratio f2/f1 was investigated by changing f1 or f2 only (fixed f2 or fixed f1 paradigm, respectively), and by changing both primaries at a fixed ratio and looking at different order DPOAE. When f2/f1 is varied in the fixed ratio paradigm, the patterns of 2 f1-f2 fine structure vary considerably more if plotted as a function of f2 than as a function of fDP. Different order distortion products located at the same characteristic place on the basilar membrane (BM) show similar patterns for both, the fixed-f2 and fDP paradigms. Fluctuations in DPOAE level up to 20 dB can be observed. In contrast, the results from a fixed-fDP paradigm do not show any fine structure but only an overall dependence of DP level on the frequency ratio, with a maximum for 2f1-f2 at f2/f1 close to 1.2. Similar stimulus configurations used in the experiments have also been used for computer simulations of DPOAE in a nonlinear and active model of the cochlea. Experimental results and model simulations give strong evidence for a two-source model of DPOAE generation: The first source is the initial nonlinear interaction of the primaries close to the f2 place. The second source is caused by coherent reflection from a re-emission site at the characteristic place of the distortion product frequency. The spectral fine structure of DPOAE observed in the ear canal reflects the interaction of both these sources.     

Distortion product otoacoustic emissions provide clues hearing mechanisms in the frog ear

2f1-f2 and 2 f2-f1 distortion product otoacoustic emissions (DPOAEs) were recorded from both ears of male and female Rana pipiens pipiens and Rana catesbeiana. The input-output (I/O) curves obtained from the amphibian papilla (AP) of both frog species are analogous to I/O curves recorded from mammals suggesting that, similarly to the mammalian cochlea, there may be an amplification process present in the frog AP. DPOAE level dependence on L1-L2 is different from that in mammals and consistent with intermodulation distortion expectations. Therefore, if a mechanical structure in the frog inner ear is functioning analogously to the mammalian basilar membrane, it must be more broadly tuned. DPOAE audiograms were obtained for primary frequencies spanning the animals' hearing range and selected stimulus levels. The results confirm that DPOAEs are produced in both papillae, with R. catesbeiana producing stronger emissions than R. p. pipiens. Consistent with previously reported sexual dimorphism in the mammalian and anuran auditory systems, females of both species produce stronger emissions than males. Moreover, it appears that 2 f1-f2 in the frog is generated primarily at the DPOAE frequency place, while 2 f2-f1 is generated primarily at a frequency place around the primaries. Regardless of generation place, both emissions within the AP may be subject to the same filtering mechanism, possibly the tectorial membrane.     

Influence of primary frequencies ratio on distortion product otoacoustic emissions amplitude. II. Interrelations between multicomponent DPOAEs, tone-burst-evoked OAEs, and spontaneous OAEs

Distortion product otoacoustic emissions (DPOAEs) are used widely in humans to assess cochlear function. It is well known that 2f1-f2 DPOAE amplitude increases as the f2/f1 ratio increases from 1.0 to about 1.20, and then decreases as the f2/f1 ratio increases above 1.20, showing an amplitude ratio function, which is thought to be related to cochlear filtering properties. Different lower sideband DPOAEs are believed to show the same amplitude ratio functions as the 2f1-f2 DPOAE, with a magnitude peak situated at a constant DPOAE frequency relative to f2. More recently, several studies have suggested the involvement of a DPOAE component coming from its own distortion product place as well as the DPOAE component coming from the f2 place. To investigate DPOAE generation sites and the importance of the DPOAE frequency place, amplitude ratio functions of 2f1-f2, 3f1-2f2, 4f1-3f2 and 2f2-f1, 3f2-2f1, 4f2-3f1 DPOAE components have been systematically studied in 18 normally hearing subjects, using an f2 fixed, f1 sweep method, and an f1 fixed, f2 sweep method, at ten different f2 frequencies. Results show a dependency of the distortion magnitude peak on f2 frequency for each lower sideband DPOAE, and a small frequency shift of the distortion peak for the high order lower sideband DPOAE components. Strong correlation between the different lower sideband DPOAE amplitude were obtained, whether they were recorded with the same f1 (and a different f2) or with the same f2 (and a different f1), suggesting that lower side-band DPOAE amplitude does not depend on small variations in the f2 frequency. Moreover, correlations between DPOAE amplitude and tone-burst evoked otoacoustic emissions (TBOAEs) are highly significant for TBOAEs centered at the f2 frequency and at 1/2 octave below the f2 frequency, suggesting some degree of importance of the cochlear status at frequencies below f2 in DPOAE amplitude. Subjects presenting spontaneous otoacoustic emissions showed a greater lower sideband DPOAE amplitude recorded for low f2/f1 ratios, and a distortion magnitude peak shifted towards higher frequencies. The best correlation between upper sideband DPOAE amplitude and lower sideband DPOAE amplitude occurred for lower sideband DPOAEs generated by an f2 frequency 1/2 octave to 1 octave below the primaries used to generate upper sideband DPOAEs, suggesting a site of generation basal to f2 for the upper sideband DPOAEs. Correlations between TBOAE amplitude and upper sideband DPOAE amplitude agreed with a site of upper sideband DPOAE generation basal to f2, and which would move with the DPOAE frequency itself.     

Psychoacoustical and ear canal cancellation of (2f1-f2)-distortion products

Level and phase of the (2f1-f2)-difference tone were measured as a function of primary-tone level using the psychoacoustical method of cancellation and the objective method of emission cancellation for four frequency separations of f1 = 1620 Hz and f2 in four subjects. Differences between hearing- and emission-cancellation levels ranged from 60-33 dB as delta f = f2-f1 increased from 180 to 432 Hz. For smaller separations of the primaries, phase changes for emission cancellation covered a wide range and had sharp "steps," whereas for hearing cancellation, the phase varied only slightly. With wider separations of the primaries, the phase became more varied for hearing cancellation and more homogeneous for emission cancellation. Both emission- and hearing-cancellation level functions were nonmonotonic as a function of constant SL1 and varied SL2. Remarkable phase shifts always appeared near minima in level at all separations of the primaries for emission cancellation. Four sources may be contributing to the differences in results: (a) the frequency-dependent attenuation of the middle-ear transfer function, (b) the frequency-dependent mismatch of the acoustical impedances at the eardrum, (c) the frequency dependence of the microphone's sensitivity mounted within the probe, and (d) the different reaction of active nonlinear cochlear processes on the hearing- and emission-cancellation tones.     

Modeling the growth rate of distortion product otoacoustic emissions by active nonlinear oscillators

In this work, growth-rate curves of the 2 f1-f2 distortion product otoacoustic emission (DPOAE) are analyzed in a population of 30 noise exposed subjects, including both normal-hearing and hearing impaired subjects. A particular embedded limit-cycle oscillator equation is used to model the cochlear resonant response at the cochlear places of the primary and secondary tone frequencies (f2 and 2 f1-f2). The parameters of the oscillator equation can be directly interpreted in terms of effectiveness of the cochlear feedback mechanisms associated with the active filter amplification. A two-sources paradigm is included in the model, in agreement with experimental evidence and with the assumptions of more detailed full cochlear models based on the transmission line formalism. According to this paradigm, DPOAEs are nonlinearly generated at the cochlear place that is resonant at frequency f2, and coherently reflected at the 2 f1-f2 place. The analysis shows that the model, which had been previously used to describe the relaxation dynamics of transient evoked otoacoustic emissions (TEOAEs), also correctly predicts the observed growth rate of the DPOAE response as a function of the primary tones amplitude. A significant difference is observed between normal and impaired ears. The comparison between the growth rate curves at different frequencies provides information about the dependence of cochlear tuning on frequency.     

Short-term effects of sound exposure on the 2f1-f2 acoustic emission

The 2f1-f2 acoustic emission (AE) was recorded in the ear canals of cats following exposure to tone bursts of 200-ms duration. Exposures known to result in short-term adaptation (i.e., adaptation lasting under 1 s) at the level of the auditory nerve failed to produce significant post-exposure changes in AE amplitude. Given the apparent cochlear origin of the 2f1-f2 AE, this result is consistent with the view that short-term adaptation in the auditory periphery does not involve substantial changes in cochlear mechanics.     

Auditory efferent activation in CBA mice exceeds that of C57s for varying levels of noise

The medial olivocochlear efferent (MOC) system enhances signals in noise and helps mediate auditory attention. Contralateral suppression (CS) of distortion product otoacoustic emissions (DPOAEs) has revealed age-related MOC declines. Here, differences in CS as a function of contralateral noise intensity (43-67 dB sound pressure level) were measured; 2f1-f2 DPOAE grams were recorded for young adult CBA and C57 mice. In CBAs, CS was a monotonic function of contralateral noise level. The C57s showed normal hearing, measured with DPOAE amplitudes and auditory brainstem response thresholds, but showed little CS, suggesting a loss of efferent dynamics preceding any deficiencies of the afferent auditory system.     

Synchronization of spontaneous otoacoustic emissions to a 2f1-f2 distortion product

Synchronization of spontaneous otoacoustic emissions to a cubic distortion frequency fs = 2f1-f2 has been studied. Stimulus, consisting of two primary tones at frequency f1 and f2, could easily be filtered out of the microphone signal. This enabled us to monitor emission phase with respect to synchronization frequency fs, by recording zero-crossing moments of the microphone signal. When primaries were sufficiently loud (typically 30 dB SPL), phase fluctuated around a constant value: The emission was constantly synchronized to fs. Lowering primary levels (to typically 20 dB SPL) resulted in 2 pi-phase jumps at random moments: The emission occasionally slipped out of synchronization, trying to maintain its own natural frequency f0. This behavior can be described as synchronization of an oscillator (frequency f0) to a sinusoidal force (frequency fs) in the presence of noise.