Hearing and Deafness 2. Ear as a frequency analyzer
Chris Darwin
Frequency: 100-Hz Sine Wave
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Frequency: 500-Hz Sine Wave
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Amplitude: 500-Hz Sine Wave
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Phase: 500-Hz Sine Wave
The amplitude spectrum does not show phase
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sine
cosine
adding sine waves
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Spectrum of Sum
100-Hz fundamental Complex Wave
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Adding nine sine waves
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Spectrogram 5s
5s
The linear vs log scales
Linear
• equal distances represent equal differences
0 100 200 300 400 500
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)
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Bandpass filtering (wide)
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Repetition rate is the difference in frequency between the two sine-wave components
1/3 second 505 - 500 = 5 Hz
Beats
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Repetition rate is the difference in frequency between the two sine-wave components
1/100th second 500 - 400 = 100 Hz
400
Reponse of basilar membraneto 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)
QuickTime™ and aAnimation decompressor
are needed to see this picture.
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
A gardening analogy
A gardening analogy
Auditory bandwidth
Noise bandwidth
Detection mechanism
Tone
Noise
Wider auditory filter
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
Conductive vs Sensori-neural deafness
Conductive Sensori-neural Sensori-neural
Origin Middle-ear Cochlea (IHCs) Cochlea (OHCs)
Thresholds Raised Raised Raised
Filter bandwidths Normal Normal Increased
Loudness growth Normal Normal Increased (Recruitment
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