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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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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Beats

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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

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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