Biophysics Laboratory Manual
Experiment 5 - The Frequency Response of the Auditory System
The auditory system as a frequency analyser
The ear responds to small temporal fluctuations in atmospheric pressure, which range on a
time scale from hundredths to millionths of a second. Since biological receptor cells and
neurones cannot respond to such rapid signals, the ear carries out a partial Fourier analysis,
or spectral analysis, of the sounds it receives. It smears these Fourier analyses out over a
period of the order of ten milliseconds, reducing the required response rate in the receptor
cells to around this order, at the expense of having to operate many channels each tuned to
a different frequency. Hence we find it convenient to speak of the frequency response of
the ear, rather than of its temporal response capabilities.
In this prac you will determine first the overall frequency response of your own ears and
then the frequency response of a single analysis channel. Both of these are done by simply
listening to a pulsed tone and adjusting its loudness until you can just hear it. The tones are
presented one ear at a time through headphones and are generated by the computer's sound
system.
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Logarithms and the decibel scale
The sensation of loudness increases roughly with the logarithm of sound intensity, so it has become
the convention to express sound intensity on such a scale.
A Bel is defined as the logarithm, base 10, of the ratio, of two powers, the measured power and a
reference power. i.e.
P1
Bels = log10 P 
 2
where P1 is the power beaing measured, and P 2 is the reference power.
The Bel is too large a unit for convenient use, so the decibel is commonly used. It is simply 10 times
the Bell i.e.,
P1
decibels = 10 log10 P  .
 2
It is more convenient to measure the pressure of a sound wave than its power flux, so, since power is
proportional to pressure squared, the decibel is defined as 20 log(p 1/p2) where p1 is the measured
pressure and p2 is the reference pressure.
Sound Pressure level (SPL) is defined as the ratio of the measured pressure to a reference of 2.0 x 105 Pa, close to the threshold of hearing at 1 kHz.
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General notes
In determining the softest tone level you can hear, listen carefully and to several
presentations of the tone. You may find you can hear it only on occasional presentations,
not every one. That's fine, your ear is not as deterministic as an optical spectrum
analyser and you are searching for the softest sound you can hear at all.
You may also sometimes be unsure if you can hear the tone. Don't worry about this
either, just increase the loudness slightly and try again. You should aim to find the
softest sound you can sometimes hear. Don't be too concerned with the exact threshold the minimum step size you will use is 3 decibels and this is of the order of accuracy
available.
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Take your time! You could rush through this prac in half an hour, but if you are careful
and do each measurement carefully, you will achieve much better results and be more
satisfied with the outcome.
• Measurement of the auditory frequency responses
In the first part of this prac. you will measure the overall frequency response of your
own ears, by adjusting the loudness of a test tone so that you can just hear it. This is
repeated for a range of frequencies, building up a pattern of how your ear responds to
different frequencies.
• Equipment
The tones are generated by the sound system of a computer and are presented to your
ears through miniature earphones. The tones are pulsed so that it is easier to hear them
when they are very soft. The calibration of the earphones is not known accurately and in
particular it is not known just exactly how loud the sounds are. We do know, however,
that any variation in efficiency of the earphones with frequency is very small compared
with that of your ears, so it may be ignored for the present purposes. Also, thresholds are
remarkably consistent across normal individuals, so by comparing your results with
those of the rest of your group you may 'calibrate' the earphones to absolute Sound
Pressure Level (SPL).
• What the experiments consists of
The sounds are short pulses of sine-wave signals, with gradual onset and offset ramps.
Without the gradual onset and offset you would hear 'clicks' and this would confuse your
estimates of threshold. Each tone pulse is (in general) of a different frequency and
amplitude and is independently controllable. The rise/fall times are 10 ms for both and
the second tone has only a rise and a fall period: it has no steadystate period.
100 0
p
500
0
-500
-100 0
0
50
t (ms)
100
150
200
• Running the test program
The program is run by doubleclicking the mouse button on the icon named
"audiology_lab"
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From within the program (Igor) select "start" from the menu "Macros".
Test Ear:
The popup option determines whether sound is applied to the left, right or both ears.
You will determine responses for both left and right ears separately but, for this prac.
class you will not use the button labelled Both.
First Tone:
This controls the test tone used for determining overall thresholds, and for forward
masking when determining channel tuning.
The spin control marked Frequency adjusts the frequency of the first tone in 100 Hz
steps. Initially it should be set to 100 Hz.
The spin control marked Intensity adjusts the loudness of the first tone, in 1 dB steps.
The numbers represent approximate† SPLs and may range from -12 to +70 dB. Initially it
should be set to about 40.
Second Tone:
This controls the second tone, used as the probe tone in the second part of the prac. For
the first part it should be turned off (pulse 2 unticked).
Part I. Measurement of overall frequency response
The overall frequency response of the ear is the range of frequencies you can hear when
each frequency is presented alone, and its definition also usually includes the sound
pressure level necessary for you to just hear it.
The overall frequency response is determined by several stages, all acting on the sound
as it travels from the air to the auditory nerve.
the pinna
The pinna is what you normally see of the ear, and what most people refer to as 'the ear'. It is the
flap of cartilage which sits each side of your head. Its function is to intercept the sound field and so
increase sensitivity, and to act as a complex, highly directional reflector of high-frequency sounds
from which you can determine the position of a source of sound.
the external ear canal
The external ear canal, or external auditory meatus, is the canal down which sound travels after
being intercepted by the pinna. Terminating the meatus is the ear drum, or tympanic membrane, a
thin membrane which is pushed in and out by the sound pressure fluctuations. The prime function of
the meatus is to protect the tympanic membrane from damage by keeping away sharp objects and
insects. Acoustically, it is a tube closed at one end and hence it functions like an open organ pipe
(open at one end, that is) tuned to approximately 4-6 kHz.
the middle ear
The middle ear is a cavity within the skull, bounded at one place by the tympanic membrane. It
houses the 3 middle ear bones, or ossicles: the manubrium (or hammer), the incus (or anvil) and the
stapes (or stirrup) which conduct the motion of the tympanic membrane through to the cochlea.
Mechanically, the middle ear ossicles behave as a resonant mass-spring-damper system, although
they are heavily loaded by the cochlea. For frequencies below, say, 3 kHz, the elasticity of the
middle ear limits the excursion under sound pressure, while somewhat above that frequency it is the
mass which limits displacement. For higher frequencies again, the resistance of the cochlea
dominates.
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the cochlea
The cochlea is a long, narrow, coiled chamber, filled with a fluid (chiefly water). It is split
along its length by the basilar membrane which forms the basis for the frequency analysis
performed in the ear. The basilar membrane carries a strongly dispersive (i.e., its velocity is
dependent upon frequency) wave, known as the travelling wave.
Turn the second tone off by unclicking the pulse 2 box. Then set the frequency of the first
tone to 100 Hz and the intensity to 40 dB. From now on keep as still and quiet as you can
since extraneous noise will 'mask' or cover up the sounds you are listening for.
Your will hear the tone pulsating at a rate of about twice a second. Slowly adjust the
intensity of the first tone downwards until you can just hear it. Track up and down once
or twice until you are sure you have threshold. Don't be concerned that you dont hear it
every time, just so long as you can usually hear it. Record the frequency and SPL of this
first tone in the table provided and then change the frequency to the next on the table.
Repeat this for all frequencies and then start over again for the right ear.
• Interpreting the response
Now plot each point on the graph provided - the one marked Overall Frequency
Response. Compare the results from each ear with the Fletcher-Munsen curve. This curve
is an internationally-recognised standard for a 'normal' ear, derived by measuring many
individuals with normal hearing.
Assuming your ears are normal, the data for both ears will follow the Fletcher-Munsen
curve (already drawn of the graph), but perhaps a little above or below it. (The is mostly
due to inaccurate calibration† of the earphones.) Notice several things about the results.
• The sensitivity is lower (the threshold SPL is higher) for the lower frequencies. This is
due mostly to the elastically-limited displacement of the middle ear.
• The sensitivity flattens to a mid-range region where it is almost independent of
frequency. In this range the elastic properties of the middle ear are over-ridden by its
inertia, and by the resistance of the cochlea carrying energy away along the travelling
wave.
• At high frequencies the sensitivity again falls, due to a fall in the efficacy of the
mechanical amplification taking place within the cochlea.
frequency response is not the same for all loudness levels
If the frequency response of the ear were measured for a range of intensities, we would
find that the overall frequency response depends upon the intensity. Louder sounds vary
less in their perceived loudness with frequency. This is due to the nonlinearity of the
cochlear amplifier.
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Part II. measurement of the frequency response of a single channel
• The ear as a frequency-analyser
As we have already described, the ear functions as a Fourier analyser to convert an
incoming channel of rapidly-fluctuating signals into many channels of more-slowly
fluctuating responses. Each channel encodes the activity in a particular frequency band
of the sound stimulus. In the second part of this prac. we will use a trick to determine
the frequency responses of some of these channels.
• 'Line-busy' effect with hangover
When a channel is stimulated into activity its sensitivity to other signals which might
also be present in the channel is reduced. This is known as a 'line-busy' effect, in
analogy with a telephone line which can only be used for one conversation at a time. In
the case of the auditory channels, however, the line-busy effect hangs on for about 5 - 40
ms after termination of the stimulus, so that a new stimulus following closely after may
not be heard. This effect is known as forward masking, because the masking effect is
caused by something which happened earlier.
equipment
Exactly the same equipment is used as in part I, but this time we adjust the amplitude of
the first tone until we can no longer hear the second tone. The idea is that we set the
second tone, which is very short, at an intensity just above its threshold. We precede it
with the first tone and increase the intensity of the first tone until it just hides, or masks,
the second. If the first tone stimulates activity in the channel, it will stop you hearing the
second because of the line-busy effect.
initial preparation
Set the intensity of the first tone to -12 dB. Set the frequency of the second tone to 1000
Hz and adjust its intensity until you can just hear it (as for part 1). Now increase the
intensity by 10 dB. It should be easily audible now. Take note of sound: of the tone
because this is what you are now listening for. Make a note of the frequency
andintensity of the second tone Set the frequency of the first tone to 200 Hz and its
intensity to around 30 dB. Now gradually increase its intensity while listening for the
second tone. Adjust the intensity of the first tone until it just masks the second. This
takes a little practice. Take your time. If you are not sure if you can hear the second
tone, try changing its frequency up and down by a single 100 Hz step, since a little
novelty helps the auditory system considerably. When you can no longer hear the
second tone, write down the intensity of the first tone in the table provided. If you can
still hear the second tone at the loudest intensity of the first, then record the result with
an up-arrow (^| ) to indicate that it was higher than the equipment would produce.
Now step the first frequency up by 100 Hz and repeat. Continue stepping the frequency
of the first tone until it is above the second frequency. Your results will tell you when
you have gone high enough.
You have now completed measuring a single-channel frequency response for the 1000
Hz channel. Now step the second frequency to 2,000 Hz, again set it at 10 dB above
threshold, and repeat the whole procedure. Do this for further frequencies of 4,000 and
8,000 Hz.
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interpreting the response
Plot the four single-channel response curves on the lower chart provided. Since this is a
masking experiment the filter shapes are inverted from what you might normally expect.
The most-sensitive part of the reponse is plotted lowest on the graph (think of it as a
filter response curve plotted upside-down).
Notice that each is a very-sharply tuned filter, rejecting frequencies either side of the
best frequency. The frequency at which the least intensity of tone 1 was required should
be the same as, or very close to, the frequency of the second tone. If you have already
had the lectures on auditory biophysics you might think about why the frequencies may
not be identical.
For each curve, calculate the following parameters:
• Sl, the slope in decibels per octave, of the low-frequency side. Measure this over a
range from, say, 10 dB above the tip of the curve to, say, 40 dB above the tip. Compare
this with the slope you would expect from a simple mechanically-resonant filter.
• Sh, the slope in decibels per octave, of the high-frequency side using similar limits.
• W10dB, the width of the response curve, in Hz, 10 dB above the tip.
• W40dB, the width of the response curve 40 dB above the tip.
Notice that the bandwidth of each channel increases in absolute terms with increasing
frequency, but decreases in relative terms. The graphs you have produced have a
logarithmic frequency scale and so the filters look to be narrower as the channel
frequency increases.
____________________
†
Note on units used in the program. Normal CD audio is digitised in two (L&R)
channels each sampled 44100 times a second with each sample represented by a 16 bit
number. This means the sampled voltage is converted to an integer between -32767 and
+32768. For this prac we use a reference level of 10. Thus for example an amplitude of
10000 is shown as:
10000
20 log  10  = 60 dB .


Similarly an amplitude of 20 corresponds to +6 dB. You will need to calibrate this scale
by making a measurement with the sound pressure level meter.
calibration procedure.
Set the pulse 1 frequency to 1000 Hz and the amplitude to 60 dB. Turn off pulse 2.
Carefully arrange for the enabled headphone (L or R) to sit flush with the pressure level
meter's microphone. Set the meter to the highest setting (110 dB) and FAST. Run the
pulse in repeat mode and record at least 6 readings. From the average value you can
now convert all of your screen readings to SPL.
Graeme Yates 1995, Ralph James 2002
Biophysics Laboratory Manual