Hearing and Deafness 2 Ear as a frequency

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

Frequency: 100 -Hz Sine Wave 1. 0 Spectrum 0 Amplitude against frequency -1. 0 0 Time (s) Waveform 0. 05 1 amp Amplitude against time 100 Hz frequency

Frequency: 500 -Hz Sine Wave 1. 0 Spectrum 0 Amplitude against frequency -1. 0 0 Time (s) 0. 05 1 Waveform amp Amplitude against time frequency 100 500 frequency

Amplitude: 500 -Hz Sine Wave Spectrum Amplitude against frequency 0 1 0 Time (s) 0. 05 amp frequency 100 0 0 Time (s) 0. 05 500 frequency

Phase: 500 -Hz Sine Wave sine The amplitude spectrum does not show phase 1 amp cosine frequency 100 500 frequency

adding sine waves Spectrum of Sum 1 amp frequency 1 amp

100 -Hz fundamental Complex Wave 5. 0 Spectrum Amplitude against frequency 0 -1. 7 0 Time (s) Waveform 0. 05 1 amp Amplitude against time frequency 100 500 frequency

Frequency Adding nine sine waves Time 5 s Frequency Spectrogram

The linear vs log scales Linear • equal distances represent equal differences 0 100 200 300 400 500 100 -1 200 0 400 1 800 2 1600 3 3200 4 Log • equal distances represent equal ratios e. g. Piano keyboard frequencies Octave = doubling of frequency basilar membrane has log repn of frequency

deci. Bel (d. B) scale Sound A is x d. B more intense than sound B when: x = 10*log 10 (energy of A / energy of B) or x = 20*log 10 (amp of A / amp of B) So if A is 20 watts and B is 10 watts x = 10*log 10 (20/10) = 10*0. 3 = 3 d. B You can usually just hear a difference of 1 d. B (jnd)

Bandpass filtering (narrow) 5. 0 1 amp 0 -1. 7 0 Time (s) 0. 05 frequency 100 500 frequency 1 amp 0 0 Time (s) 0. 05 frequency 100 500 frequency

Bandpass filtering (wide) 5. 0 1 amp 0 -1. 7 0 Time (s) frequency 100 0. 05 500 frequency 1 amp frequency 100

Beats Repetition rate is the difference in frequency between the two sine-wave components 1/3 second 505 - 500 = 5 Hz 1 amp frequency 100 500 frequency

Beats Repetition rate is the difference in frequency between the two sine-wave components 1/100 th second 500 - 400 = 100 Hz 1 amp frequency 100 400 500 frequency

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 1000 Hz 250 Hz Broadband Noise frequency 2000 Hz Amadeus

A gardening analogy

A gardening analogy

A gardening analogy Tone Noise Auditory bandwidth Noise bandwidth Detection mechanism

Wider auditory filter

Auditory tuning curves Inner hair-cell damage Healthy ear

Outer-hair cell damage

Human auditory bandwidth At 1 k. Hz the bandwidth is about 130 Hz; at 5 k. Hz 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

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

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