Test your Ears: About our Hearing
When
measuring sound and how our ears respond to it the most important
notions are the Sound Pressure Level, SPL
and the Loudness.
SPL
is an objective physical property, which indicates the acoustical power
of a certain sound. It is given mostly in dB where 0
dB is related to a
sound pressure of 20 micro-pascal. That is about the weakest
sound the human ear can detect under the most favorable conditions at
2 -
4 kHz. (1 pascal = 1 Newton per m2)
SPL goes with the square
of the actual sound pressure in Pascal. That is because there
is
another player in the game, which is the velocity with which the
air-particles move. The acoustical power is the product of that
pressure and that velocity. The velocity is proportional with the
pressure in Pascal, because the relation between these two, the
acoustical impedance, is a constant for air at atmospherical pressure.
{Actually
there is confusion about the terminology. SPL is actually
power density, although it suggest to be only the pressure, and is
often given in (micro) Pascal. Sound Pressure is the pure pressure
measured in (micro) Pascal. Particle Velocity is rarely mentioned,
because, for air at atmospherical pressure, it is directly proportional
to the Sound Pressure (The proportionality factor is the Acoustic
Impedance). SPL is the product of Pressure and Particle Velocity and
should be given in Watts/m2, but than it is called Intensity.
Congratulations if you understand it now }
Sound
Pressure, Particle Velocity and SPL
are always given as RMS values.
Below is a table with the relations.
|
Pressure [Pascal] |
Velocity [m/s] |
Intensity [W/m2] |
SPL [dB] |
Remark |
|
200 |
5 x 10-1 |
100 |
140 |
Above the
threshold of pain. |
|
20 |
5 x 10-2 |
1 |
120 |
|
|
2 |
5 x 10-3 |
10-2 |
100 |
|
|
2 x 10-1 |
5 x 10-4 |
10-4 |
80 |
|
|
2 x 10-2 |
5 x 10-5 |
10-6 |
60 |
|
|
2 x 10-3 |
5 x 10-6 |
10-8 |
40 |
|
|
2 x 10-4 |
5 x 10-7 |
10-10 |
20 |
|
|
2 x 10-5 |
5 x 10-8 |
10-12 |
0 |
Approximately
the threshold of human hearing. |
Loudness
is the subjective experience of the intensity af a sound. That
experience depends
quite strongly on the frequency, the
pitch of a
sound.
The relation between SPL and the loudness as a function of
frequency is given for the human ear by the Fletcher-Munson graphs.
These graphs were created from measurements on many people. From these
graphs one can conclude that the subjective experience is widely
different for frequencies deviating from 1 kHz (note 1).
Especially at lower frequencies the sensitivity of our ears decreases
with lower frequencies, and even the faster with lower sound
intensities.
The lowest line in the Fletcher-Munson graphs depicts the hearing
threshold. That is the lowest sound level humans can detect in an
extremely silent environment.
(Note
1)
This
property of the human hearing has led to all kinds of experiments for a
so called "physiological volume control" in audio amplifiers. Ideally,
when lowering the volume, the highest and lowest frequencies should be
attenuated less than the mid-range, such that the subjective
experienced balance between high and low frequencies is preserved.
Most of these experiments have failed.
The "loudness" switch
found on many amplifiers should have more-or-less of this function -
lowering everything, but less for the highest and lowest frequencies- ,
but for commercial reasons it does not lower
the all-over volume, but
only emphasizes the lowest and highest frequencies, so you wil have an
unnatural thick and fat sound, but not a lower
volume.
Fig
1. The Fletcher-Munson
graphs. The waving lines depict the SPL, Sound Pressure Level,
required to obtain a certain loudness in (Foon) Phon of Soon .
(The Soon
is somewhat obsolete and not logaritmic)
For example, to experience a loudness of 40 Phone at 1 kHz an SPL of 40
dB is required. At 20 Hz however we need over 90 dB !
Below is a list for a rough impression about how
load several sounds are
140 dB Threshold of pain
120 dB Jet airplane passing at low altitude
100
dB
Passing truck at small distance
Loudest sound measured by the author in the Amsterdam
Concerto Building during a concerto. I was sitting on the balcony,
almost
above he
orchstra.
80
dB
Speaker adressing a large puplic, at 1 meter
distance.
Dutch
laws demand sound
protection measures in working situations when SPL's are over 80 dB.
60 dB
Quit conversation.
40
dB
Very quite room. Hardly any sound from outside. In an
inner-city-home this level will be trespassed often, even at midnight.
20
dB
Rustling leaves, almost windstil, calm.
3
dB
Hearing Threshold.
When professionally diagnosing hearing problems the main issue is the hearing threshold. An increase at certain frequencies is an indication for more-or less serious hearing damage. Audiologists (the specialists in this field) primaraly look for hearing loss at frequencies which are important for understanding human speech, because this has the most far-going social consequences. Roughly this is the frequency range from 200 Hz to 8 kHz.
In many cases hearing damage can be remedied by a hearing aid, an electronic device which amplifies the frequencies which are lost. Modern hearing aids can be carried almost invisible, so there is no reason for shame.
The
most frequent hearing problems are caused by elderness and
in younger people by exposion to excessive sound
levels in
the working environment or by visiting disco's and pop-concertos, but
also by the use of "personal audio" devices at a much to high SPL.
Don't think that it's only pop-music attacking your ears. The
audiologist's waiting rooms are also populated by musicians from the
well known classical symphony orchestras. E.g. some of them sit
directly in front of the trumpets, and what about the large
cymbals?
A
hearing problem which cannot be listed as a damage but can be very
annoying is known as tinnitus. A frequent version is where you
constantly hear a high-frequency beeping, somewhat like from a rack
with switched-mode-power supplies at 8 kHz or so.
Other
measurable properties of the human hearing are primarely
masking
effects. That means that in the presence of a certain sound A you are
not able to detect another sound B, depending on the sound levels and
frequencies of A and B.
Also there are effects of temporal
masking. When a sound A is rapidly followed by a sound B, the B cannot
be detected depending on the time difference between A and B, and the
sound levels, frequencies and durations of the sounds.
Masking
effects can be measured on one ear, on both
ears simultaneously, or between the ears, that is, when one
ear
gets the masking sound and the other ear gets the sound to be masked.
Many
insights about how our hearing works (these are the mechanisms in the
cochlea, but also the further processing in the brain) have been derived
from such measurements, done with healthy people and with people with a
hearing disorder.
Another
aspect is how we experience the direction from which the sound comes.
It appears that time-of-arrival differences plays an important role (a
sound
from left arrives earlier at the left ear), but also the sonic
differences are important. A sound from the left has to run around the
head to reach the right ear, and looses in particular some of the higher frequencies.
And -last but not least- we have the so called A-B-X-tests, where you
hear sounds A and B, you are told what A and B are,
and then
you hear X
and you have to guess whether X=A or X=B. The question
is: How well are you able to uniquely distinguish between A
and B, or in other words, how different are A and B.
You
may think of music fragments (A) with a deliberate amount of distorsion
added (B) or pieces of music recorded with different
compression
techniques.
For many such tests the reproduction of the sound
can be done with a (hifi) audio amplifier and the (hifi) loudspeakers in your
living room.