Skip to main content
. 2019 Sep 24;8:e47667. doi: 10.7554/eLife.47667

Figure 2. Three causes of magnitude scatter in DP2 spectra.

(A) Combinatorial effect illustrated by feeding an equal-amplitude zwuis tone complex to a nonlinear circuit comprising a rectifier and low-pass filter (corner frequency 2.5 kHz). The 2nd harmonics (solid circles) are 6 dB weaker than the remaining DP2s (red diamonds). (B) Vector addition of DP contributions along the traveling wave (left to right). Lower row of ‘clocks’ depict amplitude and phase of the primaries f1,f2 <<CF. They accumulate little phase and their amplitude hardly grows upon traveling. Upper clocks depict a near-CF DP2 at f1+f2. Colors indicate the origin of each local contribution. Near-CF DP2 components suffer considerable phase accumulation and amplitude variation while traveling. The eventual amplitude (rightmost location) is the vector sum of multiple contributions widely differing in phase and amplitude. This interference obfuscates the spectral properties of DP2 generation investigated here. (C) Unequal primary amplitudes entering the nonlinear circuit generate a predictable scatter in DP2 magnitudes (see text). Companion phases are not affected by lack of equalization of the input. The 0.5-cycle low-frequency limit of the phase reflects the ‘negative polarity’ of the rectification.

Figure 2.

Figure 2—figure supplement 1. Propagation of DP2s in the 18-25-kHz region.

Figure 2—figure supplement 1.

Recordings were made at 9 adjacent longitudinal locations spanning ~400 μm. Phase (upper row) and magnitude (lower row) are shown of: 6 example DP2 components (red diamonds); its two parent primaries f1 and f2 (open black circles); phase and amplitude predicted by Equation 1, that is assuming local generation (black line); a reference acoustically presented component of approximately the same frequency (blue circles). DP frequency is indicated above each phase graph. For the lowest DP2 frequencies (1.3-10.4 kHz) the actual DP2 phase matches the prediction within ~0.05 cycle. For the higher DP2 frequencies systematic deviations occur. The phase accumulation of the high-frequency DP2s matches the phase of the acoustic reference much better than the prediction based on local generation. Thus these high-frequency DP2 components are dominated by their own propagation rather than local contributions from the primaries as in Equation 1. The increasing dominance of propagation with increasing DP2 frequency was observed for all DP2s.

Figure 2—figure supplement 2. Comparison of linear response components and second-order distortion products (DP2s).

Figure 2—figure supplement 2.

Data from recording shown in the lowest curves in Figure 4A–C (CF = 25 kHz; estimated cutoff frequency, 3006 Hz). (A–K) The DP2s are split according to their ‘heritage’ and the linear response components (‘parents’) are also shown. In A all the DP components relating to the lowest primary are shown. In B, that lowest primary is excluded and all the DP components relating to the new lowest primary are shown, and so on through panel K. Diamonds, linear response component (primary response) measured in the hotspot (OHC/Deiters’ region). Squares, primary response measured on the basilar membrane (BM). Circles, difference tones at f2- f1 measured in the hotspot. Plus signs, sum tones at f1+ f2 measured in the hotspot. The solid lines in all panels are identical; they show the effective OHC input determined from the DP2 spectrum. Their overall magnitude is unknown; the vertical position of the curves is chosen halfway the linear responses of BM and hotspot to facilitate comparison. The DP2s are split according to the lower primary f1. The filled symbol in each panel marks the f1 of all the DP2 components in that panel. The colors of the DP2s at f1+ f2 (plus signs) and f2- f1 (circles) match the colors of the linear responses at f2 in the same panel. (L) Detailed comparison between effective OHC input and primary responses. The effective OHC input (red lines) is shown at two different vertical positions: shifted for maximum overlap with primary responses at the hotspot (diamonds) and the BM (squares). The overlap is better for the BM data (RMS deviation, 0.9 dB) than for the hotspot data (RMS deviation, 1.9 dB).