Fig 1.
Sound waves have predictable behaviors when they encounter flat, convex, or concave reflective surfaces.
The angle of incidence equals the angle of deflection [8].
Fig 2.
Sound waves response to groove arrays.
(A) The direction of travel varies for different wavelengths. When a 40kHz harmonic series contacts a 3mm width groove array, the harmonics have different 1st order exit angles which can be calculated in relation to the 40 kHz fundamental and the angle of incidence is normal (= 0°). Because the wavelengths of the first two harmonics (40 and 80 kHz wavelengths = 8.575mm and 4.2875mm) are too large to diffract from a 3mm width groove, diffraction occurs for all harmonics above the 3rd harmonic out of each groove. For clarity we only show the response from a single groove, but this would result from every groove. (B) Waves expanding from the grooves contact each other in organized patterns. As the number of grooves increases these patterns multiply. For clarity we show the pattern of interaction from just two grooves.
Fig 3.
Two equal wavelengths of equal amplitude, will either double the amplitude during fully constructive interference when they are exactly in phase or completely cancel during fully destructive interference when exactly out of phase. Superposition of non-identical waves exhibits irregular patterns integrating both constructive and destructive interference.
Fig 4.
Groove array variations in the ears of bats and owls.
(A) Groove array variations in bat pinnae. Owl museum specimen photos show periodic structures formed where quills anchor into the skin bordering the auditory openings for (B) Long-eared Owl (Asio otus), (C) Great Grey Owl (Strix nebulosa) and a computer rendering of (D) Barn Owl (Tyto alba) where feather shafts on the operculum and quill shafts bordering the auricular opening create periodic array structures.
Fig 5.
Examples of pinna model variations and dimensions with microphone set up.
Table 1.
Ten different pinna model configurations were tested.
Fig 6.
Signal response difference graphs of the smooth model compared to the nine models with grooves.
Amplitude in decibels (dB) at 5 different frequencies comparing 9 different pinna models (see Table 1) to that of the smooth model. Each model was exposed to a 40 kHz continuous tone with five harmonics at five different distances. When smooth model amplitudes are more intense, they drop below zero.
Fig 7.
Spectrograms, power spectra and a difference graph comparing the 3mm10G pinna model and the smooth pinna model when exposed to a sound that mimics prey rustling in leaves.
Spectrograms and power spectra of the 3mm10G pinna model (A) and the smooth pinna model (B) exposed to manufactured prey sounds at a distance of 20 cm. The circled areas indicate amplitude differences between the models. The frequency difference graph (C) plots the frequency (kHz) differences in amplitude (dB) between the grooved and the smooth model. Amplitudes above the 0 dB line are stronger in the 3mm10g model; amplitudes below the 0 DB line are stronger in the smooth model.
Fig 8.
Groove number amplitude comparisons from the 40 kHz continuous tests.
Amplitude in decibels (dB) of 40 kHz continuous tone sound waves with harmonics generated at 40 cm distance and reflected by pinna models with 5,10, and 20 grooves. Groove separation was 1 mm (A), 1.7 mm (B), and 3 mm (C). The strongest signal responses denoted in dB are closer to zero.
Fig 9.
Groove width amplitude comparisons from the 40 kHz continuous tests.
Amplitude in decibels (dB) of 40kHz continuous tone sound waves with harmonics generated at 40 cm distance and reflected by pinna models with groove separations of 1 mm, 1.7 mm, 2.8 mm, and 3 mm for pinna models with 5 grooves (A), 10 grooves (B), and 20 grooves (C). The strongest signal responses denoted in dB are closer to zero.