Biomedical Engineering Reference
In-Depth Information
(a)
(b)
0
time (s)
0.003
0
time (s)
0.003
Fig. 1.3. Noise vs. pitched sound waves. ( a ) A very irregular sound wave (here,
the wind recorded in the field) is what we call “noise”. ( b ) In contrast, when the
sound wave is regular or periodic (such as the fraction of the great grebe's song
shown here), our ear is able to recognize a pitch, and we call it a “note”
that emerges from a comparison between the two records is the existence of a
regularity in the second one. This record is almost periodic , i.e., it has similar
values at regular intervals of time. This periodicity is recognized by our ear
as a pure note. In contrast, when the sound is extremely irregular, we call it
noise.
Let us describe pure notes. The periodicity of a signal in time allows us
to give a quantitative description of it: we can measure its period T (the time
it takes for a signal to repeat itself) or its frequency f , that is, the inverse
of the period. The frequency represents the number of oscillations per unit
of time, and is related to the parameter ω (called the angular frequency )
through ω =2 πf . If time is measured in seconds, the unit of frequency is
known as the hertz (1 Hz = 1/s). What does this mean in terms of something
more familiar? Simply how high or low the pitch is. The higher the frequency,
the higher the pitch.
Let us assume that the pure note corresponds to a traveling wave. In this
case, the periodicity in time leads to a periodicity in space. For this reason,
one can define a wavelength in much the same way as we defined a period for
the periodicity in time. The meaning of the wavelength λ is easily seen by
taking an imaginary snapshot of the sound signal and measuring the distance
between two consecutive crests. It has, of course, units of distance such as
meters or centimeters. A related parameter is the wavenumber k =2 π/λ .
The wavenumber and angular frequency (and therefore the wavelength and
frequency) are not independent parameters; they are related through
ω = ck ,
(1.9)
where c is the only parameter appearing in the wave equation (1.7), that is,
the sound velocity.
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