Biomedical Engineering Reference
In-Depth Information
(a)
Pain
Rock concert
130 dB
115 dB
(b)
Conversation
65 dB
Maximum audible
frequency
Mumble
20000 Hz
25 dB
Minimum audible
intensity
0 dB
Canary
6000 Hz
Soprano
Minimum audible
2000 Hz
20 Hz
frequency
Fig. 1.4. Intensity and frequency ranges for the human ear. ( a ) The intensity scale
starts at 0 dB, which does not mean the absence of sound but is the minimum
intensity for a sound to be audible. A sound of 130 dB or more (the pain threshold)
can cause permanent damage to the ear even if the exposure is short. ( b )The
minimum frequency of a pure sound for which our ear can recognize a pitch is
around 20 Hz, that is, a wave oscillating only 20 times per second. The highest
audible frequency for humans is around 20 000 Hz, although this depends on age,
for instance. Unlike bats and dogs, birds cannot hear frequencies beyond the human
limit (known as ultrasonic frequencies)
more than the period and the intensity to describe a sound. What is missing?
What do we need in order to describe the timbre ?
According to our description, the pitch of a note depends on the time
it takes for the sound signal to repeat itself, i.e. the period T . But a signal
can repeat itself without being as simple as the one displayed in Fig. 1.3b. In
Fig. 1.5 (top curve), we show a sound signal corresponding to the same note
as in Fig. 1.3b. The period T is indeed the same, but the signal displayed in
Fig. 1.5 looks more complex. It is not a simple oscillation, and in fact we show
in the figure that the signal is the sum of two simple oscillations. The first of
these has the same period as the note itself. The second signal has a smaller
period (in this case, precisely half the period of the note). If a signal repeats
itself after a time T/ 2, it will also repeat itself after a time T . Therefore,
the smallest time after which the complex signal will repeat itself is T .Our
composite note will have a period T , as in the signal displayed in Fig. 1.3b,
but it will sound different. The argument does not restrict us to adding two
simple signals. We could keep on adding components of period T/n ,where
n is any integer, and still have a note of period T . The lowest frequency
in this composite signal is called the fundamental frequency F 1 =1 /T ,and
the components of smaller period with frequencies F 2 =2 /T , F 3 =3 /T ,...,
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