Origin of the bell-like dependence of the DPOAE amplitude on primary frequency ratio

For low and medium sound pressure levels (SPLs), the amplitude of the distortion product otoacoustic emission (DPOAE) recorded from guinea pigs at the 2f₁-f₂ frequency is maximal when f₂/f₁ ≈ 1.23 and decreases for lower and higher f₂/f₁ ratios. The high-ratio slope of the DPOAE dependence on the ratio of the primary frequencies might be anticipated since the f₁ amplitude at the f₂ place is expected to decrease for higher f₂/f₁ ratios. The low-ratio slope of the dependence at low and medium SPLs of the primaries is actually one slope of a notch. The DPOAE amplitude recovers from the notch when the f₂/f₁ ratio is further reduced. In two-dimensional space formed by the f₂/f₁ ratio, and the levels of the primaries, the notch is continuous and has a level-dependent phase transition. The notch is identical to that seen in DPOAE growth functions. Similar notches and phase transitions were observed for high-order and high-frequency DPOAEs. Theoretical analysis reveals that a single saturating nonlinearity is capable of generating similar amplitude notch and phase transition when the f₂/f₁ ratio is decreased because of the increase in f₁ amplitude at the DPOAE generation place (f₂ place). The difference between the DPOAE recorded from guinea pigs and humans is discussed in terms of different position of the operating point of the DPOAE generating nonlinearity.