Hearing and Deafness 2. Ear as a frequency analyzer Chris Darwin.

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Hearing and Deafness 1. Anatomy & physiology
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Hearing and Deafness 2. Ear as a frequency analyzer Chris Darwin

Frequency: 100-Hz Sine Wave Time (s) Waveform Amplitude against time Spectrum Amplitude against frequency Hz amp frequency

Frequency: 500-Hz Sine Wave Waveform Amplitude against time Spectrum Amplitude against frequency amp frequency amp frequency500 Time (s)

Amplitude: 500-Hz Sine Wave Spectrum Amplitude against frequency amp frequency amp frequency500 Time (s) Time (s)

Phase: 500-Hz Sine Wave The amplitude spectrum does not show phase amp frequency amp frequency500 sine cosine

Phase Locking of Inner Hair Cells Auditory nerve connected to inner hair cell tends to fire at the same phase of the stimulating waveform.

Phase-locking

adding sine waves 1 amp frequency 1 amp frequency 1 amp frequency 1 amp frequency Spectrum of Sum

100-Hz fundamental Complex Wave Waveform Amplitude against time Spectrum Amplitude against frequency Time (s) amp frequency amp frequency500

Adding nine sine waves Frequency Time Frequency Time Spectrogram5s

The linear vs log scales Linear equal distances represent equal differences Log equal distances represent equal ratios e.g. Piano keyboard frequencies Octave = doubling of frequency basilar membrane has log repn of frequency

deciBel (dB) scale Sound A is x dB more intense than sound B when: x = 10*log10 (energy of A / energy of B) or x = 20*log10 (amp of A / amp of B) So if A is 20 watts and B is 10 watts x = 10*log10 (20/10) = 10*0.3 = 3dB You can usually just hear a difference of 1dB (jnd)

Bandpass filtering (narrow) Time (s) amp frequency amp frequency500 Time (s) amp frequency amp frequency500

Bandpass filtering (wide) Time (s) amp frequency amp frequency500 1 amp frequency amp frequency500

Beats 1 amp frequency amp frequency500 Repetition rate is the difference in frequency between the two sine-wave components 1/3 second = 5 Hz

Beats 1 amp frequency amp frequency500 Repetition rate is the difference in frequency between the two sine-wave components 1/100th second = 100 Hz 400

Reponse of basilar membrane to sine waves Each point on the membrane acts like bandpass filter tuned to a different frequency: high freq at base, low at apex. Each point vibrates at frequency of pure tone (-> phase locking)

Excitation patterns (envelope of excitation) Basilar membrane excitation pattern is like a spectrum

Auditory filter bandwidth (ERB)

Excitation pattern of complex tone on bm

Measurement of auditory bandwidth with band-limited noise Broadband Noise 1000 Hz 2000 Hz frequency 250 Hz Amadeus

A gardening analogy

Auditory bandwidth Noise bandwidth Detection mechanism Tone Noise

Wider auditory filter

Psychophysical tuning curves Bandwidth

Auditory tuning curves Healthy ear Inner hair-cell damage

Outer-hair cell damage

Human auditory bandwidth At 1 kHz the bandwidth is about 130 Hz; at 5 kHz the bandwidth is about 650 Hz. BW = freq / 8 roughly

Normal auditory non-linearities Normal loudness growth (follows Weber’s Law, which is logarithmic, not linear) Combination tones Two-tone suppression Oto-acoustic emissions

Combinations Tones (Tartini tones) 1 amp frequency amp frequency

Two-tone suppression

Conductive vs Sensori-neural deafness Becomes linear, so No combination tones Or two-tone suppression Mostly a combination of OHC and IHC damage

Symptoms of SNHL Raised thresholds: helped by amplification Wider bandwidths: no help possible Recruitment (restricted dynamic range): partly helped by automatic gain controls in modern digital aids Often accompanied by tinnitus

Normal vs Impaired Dynamic Range

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