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

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

Frequency: 100-Hz Sine Wave Time (s) 00.05 1.0 0 Waveform Amplitude against time Spectrum Amplitude against frequency 1 100 Hz amp frequency

Frequency: 500-Hz Sine Wave Waveform Amplitude against time Spectrum Amplitude against frequency 1 500 amp frequency 1 100 amp frequency500 Time (s) 0 0.05 1.0 0

Amplitude: 500-Hz Sine Wave Spectrum Amplitude against frequency 1 500 amp frequency 1 100 amp frequency500 Time (s) 0 0.05 0 Time (s) 0 0.05 0

Phase: 500-Hz Sine Wave The amplitude spectrum does not show phase 1 500 amp frequency 1 100 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) 00.05 -1.7 5.0 0 1 500 amp frequency 1 100 amp frequency500

Adding nine sine waves Frequency Time Frequency Time Spectrogram5s

The linear vs log scales Linear equal distances represent equal differences 0 100 200300 400 500 100 200 400 800 1600 3200 -1 0 1 2 3 4 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) 00.05 -1.7 5.0 0 1 500 amp frequency 1 100 amp frequency500 Time (s) 0 0.05 0 1 50 0 amp frequency 1 100 amp frequency500

Bandpass filtering (wide) Time (s) 00.05 -1.7 5.0 0 1 500 amp frequency 1 100 amp frequency500 1 amp frequency 1 100 amp frequency500

Beats 1 amp frequency 1 100 amp frequency500 Repetition rate is the difference in frequency between the two sine-wave components 1/3 second505 - 500 = 5 Hz

Beats 1 amp frequency 1 100 amp frequency500 Repetition rate is the difference in frequency between the two sine-wave components 1/100th second500 - 400 = 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 1 1000 amp frequency 1200 800

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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