Figure 5.1 plots the sinusoid, for , , , and. Study the plot to make sure you understand the effect of
changing each parameter (amplitude, frequency, phase), and also note the
definitions of ''peak-to-peak amplitude'' and ''zero crossings.''
Figure 5.1:An example sinusoid.
The Mathematica code for generating this figure is listed in
§5.4.
A ''tuning fork'' vibrates approximately sinusoidally. An ''A-440'' tuning
fork oscillates at cycles per second. As a result, a tone recorded
from an ideal A-440 tuning fork is a sinusoid at Hz. The amplitude determines how loud it is and depends on how hard we strike the tuning
fork. The phase is set by exactly when we strike the tuning
fork (and on our choice of when time 0 is). If we record an A-440 tuning
fork on an analog tape recorder, the electrical signal recorded on tape is
of the form
As another example, the sinusoid at amplitude and phase (90 degrees)
is simply
Thus, is a sinusoid at phase 90-degrees, while
is a sinusoid at zero phase. Note, however, that we could
just as well have defined to be the zero-phase sinusoid
rather than . It really doesn't matter, except to be
consistent in any given usage. The concept of a ''sinusoidal signal''
is simply that it is equal to a sine or cosine function at some amplitude,
frequency, and phase. It does not matter whether we choose or in the ''official'' definition of a sinusoid. You may
encounter both definitions. Using is nice since
''sinusoid'' in a sense generalizes . However, using is
nicer when defining a sinusoid to be the real part of a complex sinusoid
(which we'll talk about later).
, for
,
,
, and
. Study the plot to make sure you understand the effect of changing each parameter (amplitude, frequency, phase), and also note the definitions of ''peak-to-peak amplitude'' and ''zero crossings.''
cycles per second. As a result, a tone recorded from an ideal A-440 tuning fork is a sinusoid at
Hz. The amplitude
determines how loud it is and depends on how hard we strike the tuning fork. The phase
is set by exactly when we strike the tuning fork (and on our choice of when time 0 is). If we record an A-440 tuning fork on an analog tape recorder, the electrical signal recorded on tape is of the form
and phase
(90 degrees) is simply
is a sinusoid at phase 90-degrees, while
is a sinusoid at zero phase. Note, however, that we could just as well have defined
or
in the ''official'' definition of a sinusoid. You may encounter both definitions. Using
