= Solution
\b[Hearing requires estimating sound-producing events from noisy mixtures at two ears.] It involves mechanical detection, neural coding, source segregation and recognition. A frequency analysis alone cannot identify who or what produced the sound.
The physical input is an <acoustic pressure> fluctuation. At one ear a simplified room model is
$$
p(t)=\sum_j(h_j*s_j)(t)+n(t),
$$
where source signals $s_j$ are filtered by propagation and reflection paths $h_j$, and $n$ is noise. The <convolution> model assumes approximately linear, time-invariant propagation over the analysis interval; a moving source or listener can violate that simplification. This is a many-to-one <inverse problem>: different source configurations can produce similar ear signals. Distance, reverberation and head orientation alter a source's waveform. Pressure level is logarithmic: <sound pressure level> is $L_p=20\log_{10}(p_{\rm rms}/p_0)$, with reference $p_0=20\,\mu\mathrm{Pa}$ in air. A 100 dB difference corresponds to a pressure ratio $10^{100/20}=10^5$. The system must remain sensitive to weak signals while avoiding saturation over a large operating range.
The <middle ear> helps transfer airborne vibrations into cochlear fluids despite an <acoustic impedance> mismatch. Within the <cochlea>, the graded mechanics of the <basilar membrane> produce frequency-dependent traveling-wave responses: high frequencies peak nearer the base, low frequencies farther toward the apex. This <tonotopy> provides a distributed spectral representation. Deflection of sensory <hair cells> drives <mechanotransduction>; <inner hair cells> provide most afferent signaling, while <outer hair cells> contribute to mechanical amplification and tuning. Detection therefore depends on an active biological filter, not merely a passive bank of resonators.
A revealing experiment by <Mario A. Ruggero> and colleagues measured chinchilla basilar-membrane vibrations using the Mössbauer technique or Doppler laser velocimetry before and after a reversible intervention that reduced cochlear transduction currents. Responses near the characteristic frequency were reduced particularly strongly for weak sounds, with smaller changes at high levels and away from that frequency.<Furosemide Alters Organ of Corti Mechanics: Evidence for Feedback of Outer Hair Cells upon the Basilar Membrane by Mario A. Ruggero and others>[Abstract and response-level/frequency comparisons, J Neurosci 11, pp. 1057–1067]{ref} This supports feedback-dependent cochlear gain. The intervention also affects other cochlear processes, so it does not by itself identify every cellular contribution or directly measure human loudness. The important methodological contrast is controlled sound input plus measured mechanical output and a reversible physiological perturbation.
The resulting neural code must preserve several attributes simultaneously. Place of excitation and <neural phase locking> can provide complementary frequency and temporal information; firing rates, adaptation and population responses encode level and envelopes. Individual <neurons> have limited dynamic ranges, and temporal precision has limits. <Pitch> is not simply the location of the strongest spectral component, and <timbre> depends on spectral shape and temporal development. Even physically, a signal containing harmonics at 200 and 300 Hz repeats every 10 ms although it contains no 100 Hz component: both components complete integer cycles in that interval. Recovering source periodicity is therefore different from selecting a component in a <frequency spectrum>. It does not follow that every such signal has one obligatory perceptual <pitch>.
Localization adds ambiguity. Ear separation yields <interaural time differences>; head shadow yields <interaural level differences>; outer-ear filtering supplies direction-dependent spectral cues. In an ideal far-field point-receiver model, $\Delta t\simeq d\sin\theta/c$, obtained by dividing the path-length difference by sound speed. Real head diffraction modifies this approximation. One time difference can be compatible with several spatial directions, and phase is ambiguous when several cycles fit the delay. <Head-related transfer functions>, head movements and environmental context help resolve these ambiguities. Reverberation also requires distinguishing useful early information from later reflections.
Competing sources create both <energetic masking>, in which the target is poorly represented against overlapping acoustic energy, and <informational masking>, involving source confusion or selection despite available acoustic cues. Common onsets, harmonic relations, coherent modulation, <timbre> and spatial cues help group components into <auditory objects>. The grouping must remain stable when streams overlap, but also update when a source changes. These are the problems of <auditory scene analysis>.
<E. Colin Cherry>'s classic experiments used simultaneous spoken messages and separate messages delivered to the two ears. Asking listeners to repeat one message while ignoring the other made source selection experimentally measurable.<Some Experiments on the Recognition of Speech, with One and with Two Ears by E. Colin Cherry>[Experiments on simultaneous speech and dichotic shadowing, JASA 25, pp. 975–979]{ref} Ear and voice differences can aid selection; the result does not show that unattended information is never processed, nor that real rooms provide the clean separation of headphone channels.
Finally, meaningful recognition requires tolerance of speaker, rate and context variation. <Richard M. Warren> removed a speech segment and substituted a cough-like sound. Listeners could hear the utterance as continuous and had difficulty locating the replacement, whereas a silent interruption was more readily detected.<Perceptual Restoration of Missing Speech Sounds by Richard M. Warren>[Science 167, pp. 392–393, replacement-sound versus silence comparison]{ref} <Phonemic restoration> shows that recognition uses constraints beyond the momentary waveform; it does not mean missing acoustic information has been physically recovered. \b[Successful auditory <perception> combines peripheral sensitivity with grouping and context-sensitive inference, while retaining the possibility of masking, ambiguity and systematic error.]
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