When an alternator produces AC voltage, the voltage switches polarity over
time, but does so in a very particular manner. When graphed over time, the
"wave" traced by this voltage of alternating polarity from an alternator takes
on a distinct shape, known as a *sine wave*: Figure below

*Graph of AC voltage over time (the sine wave).*

In the voltage plot from an electromechanical alternator, the change from one
polarity to the other is a smooth one, the voltage level changing most rapidly
at the zero ("crossover") point and most slowly at its peak. If we were to graph
the trigonometric function of "sine" over a horizontal range of 0 to 360
degrees, we would find the exact same pattern as in Table below.

*Trigonometric "sine" function.*

Angle (^{o}) |
sin(angle) |
wave |
Angle (^{o}) |
sin(angle) |
wave |

0 |
0.0000 |
zero |
180 |
0.0000 |
zero |

15 |
0.2588 |
+ |
195 |
-0.2588 |
- |

30 |
0.5000 |
+ |
210 |
-0.5000 |
- |

45 |
0.7071 |
+ |
225 |
-0.7071 |
- |

60 |
0.8660 |
+ |
240 |
-0.8660 |
- |

75 |
0.9659 |
+ |
255 |
-0.9659 |
- |

90 |
1.0000 |
+peak |
270 |
-1.0000 |
-peak |

105 |
0.9659 |
+ |
285 |
-0.9659 |
- |

120 |
0.8660 |
+ |
300 |
-0.8660 |
- |

135 |
0.7071 |
+ |
315 |
-0.7071 |
- |

150 |
0.5000 |
+ |
330 |
-0.5000 |
- |

165 |
0.2588 |
+ |
345 |
0.2588 |
- |

180 |
0.0000 |
zero |
360 |
0.0000 |
zero |

The reason why an electromechanical alternator outputs sine-wave AC is due to
the physics of its operation. The voltage produced by the stationary coils by
the motion of the rotating magnet is proportional to the rate at which the
magnetic flux is changing perpendicular to the coils (Faraday's Law of
Electromagnetic Induction). That rate is greatest when the magnet poles are
closest to the coils, and least when the magnet poles are furthest away from the
coils. Mathematically, the rate of magnetic flux change due to a rotating magnet
follows that of a sine function, so the voltage produced by the coils follows
that same function.

If we were to follow the changing voltage produced by a coil in an alternator
from any point on the sine wave graph to that point when the wave shape begins
to repeat itself, we would have marked exactly one *cycle* of that wave.
This is most easily shown by spanning the distance between identical peaks, but
may be measured between any corresponding points on the graph. The degree marks
on the horizontal axis of the graph represent the domain of the trigonometric
sine function, and also the angular position of our simple two-pole alternator
shaft as it rotates: Figure below

*Alternator voltage as function of shaft position (time).*

Since the horizontal axis of this graph can mark the passage of time as well
as shaft position in degrees, the dimension marked for one cycle is often
measured in a unit of time, most often seconds or fractions of a second. When
expressed as a measurement, this is often called the *period* of a wave.
The period of a wave in degrees is *always* 360, but the amount of time one
period occupies depends on the rate voltage oscillates back and forth.

A more popular measure for describing the alternating rate of an AC voltage
or current wave than *period* is the rate of that back-and-forth
oscillation. This is called *frequency*. The modern unit for frequency is
the Hertz (abbreviated Hz), which represents the number of wave cycles completed
during one second of time. In the United States of America, the standard
power-line frequency is 60 Hz, meaning that the AC voltage oscillates at a rate
of 60 complete back-and-forth cycles every second. In Europe, where the power
system frequency is 50 Hz, the AC voltage only completes 50 cycles every second.
A radio station transmitter broadcasting at a frequency of 100 MHz generates an
AC voltage oscillating at a rate of 100 *million* cycles every second.

Prior to the canonization of the Hertz unit, frequency was simply expressed
as "cycles per second." Older meters and electronic equipment often bore
frequency units of "CPS" (Cycles Per Second) instead of Hz. Many people believe
the change from self-explanatory units like CPS to Hertz constitutes a step
backward in clarity. A similar change occurred when the unit of "Celsius"
replaced that of "Centigrade" for metric temperature measurement. The name
Centigrade was based on a 100-count ("Centi-") scale ("-grade") representing the
melting and boiling points of H_{2}O, respectively. The name Celsius, on
the other hand, gives no hint as to the unit's origin or meaning.

Period and frequency are mathematical reciprocals of one another. That is to
say, if a wave has a period of 10 seconds, its frequency will be 0.1 Hz, or 1/10
of a cycle per second:

An instrument called an *oscilloscope*, Figure below,
is used to display a changing voltage over time on a graphical screen. You may
be familiar with the appearance of an *ECG* or *EKG*
(electrocardiograph) machine, used by physicians to graph the oscillations of a
patient's heart over time. The ECG is a special-purpose oscilloscope expressly
designed for medical use. General-purpose oscilloscopes have the ability to
display voltage from virtually any voltage source, plotted as a graph with time
as the independent variable. The relationship between period and frequency is
very useful to know when displaying an AC voltage or current waveform on an
oscilloscope screen. By measuring the period of the wave on the horizontal axis
of the oscilloscope screen and reciprocating that time value (in seconds), you
can determine the frequency in Hertz.

*Time period of sinewave is shown on oscilloscope.*

Voltage and current are by no means the only physical variables subject to
variation over time. Much more common to our everyday experience is
*sound*, which is nothing more than the alternating compression and
decompression (pressure waves) of air molecules, interpreted by our ears as a
physical sensation. Because alternating current is a wave phenomenon, it shares
many of the properties of other wave phenomena, like sound. For this reason,
sound (especially structured music) provides an excellent analogy for relating
AC concepts.

In musical terms, frequency is equivalent to *pitch*. Low-pitch notes
such as those produced by a tuba or bassoon consist of air molecule vibrations
that are relatively slow (low frequency). High-pitch notes such as those
produced by a flute or whistle consist of the same type of vibrations in the
air, only vibrating at a much faster rate (higher frequency). Figure below
is a table showing the actual frequencies for a range of common musical notes.

*The frequency in Hertz (Hz) is shown for various musical notes.*

Astute observers will notice that all notes on the table bearing the same
letter designation are related by a frequency ratio of 2:1. For example, the
first frequency shown (designated with the letter "A") is 220 Hz. The next
highest "A" note has a frequency of 440 Hz -- exactly twice as many sound wave
cycles per second. The same 2:1 ratio holds true for the first A sharp (233.08
Hz) and the next A sharp (466.16 Hz), and for all note pairs found in the table.

Audibly, two notes whose frequencies are exactly double each other sound
remarkably similar. This similarity in sound is musically recognized, the
shortest span on a musical scale separating such note pairs being called an
*octave*. Following this rule, the next highest "A" note (one octave above
440 Hz) will be 880 Hz, the next lowest "A" (one octave below 220 Hz) will be
110 Hz. A view of a piano keyboard helps to put this scale into perspective:
Figure below

*An octave is shown on a musical keyboard.*

As you can see, one octave is equal to *seven* white keys' worth of
distance on a piano keyboard. The familiar musical mnemonic
(doe-ray-mee-fah-so-lah-tee) -- yes, the same pattern immortalized in the
whimsical Rodgers and Hammerstein song sung in __The Sound of Music__ --
covers one octave from C to C.

While electromechanical alternators and many other physical phenomena
naturally produce sine waves, this is not the only kind of alternating wave in
existence. Other "waveforms" of AC are commonly produced within electronic
circuitry. Here are but a few sample waveforms and their common designations in
figure below

*Some common waveshapes (waveforms).*

These waveforms are by no means the only kinds of waveforms in existence.
They're simply a few that are common enough to have been given distinct names.
Even in circuits that are supposed to manifest "pure" sine, square, triangle, or
sawtooth voltage/current waveforms, the real-life result is often a distorted
version of the intended waveshape. Some waveforms are so complex that they defy
classification as a particular "type" (including waveforms associated with many
kinds of musical instruments). Generally speaking, any waveshape bearing close
resemblance to a perfect sine wave is termed *sinusoidal*, anything
different being labeled as *non-sinusoidal*. Being that the waveform of an
AC voltage or current is crucial to its impact in a circuit, we need to be aware
of the fact that AC waves come in a variety of shapes.

**REVIEW:**
- AC produced by an electromechanical alternator follows the graphical shape
of a sine wave.
- One
*cycle* of a wave is one complete evolution of its shape until
the point that it is ready to repeat itself.
- The
*period* of a wave is the amount of time it takes to complete one
cycle.
*Frequency* is the number of complete cycles that a wave completes in
a given amount of time. Usually measured in Hertz (Hz), 1 Hz being equal to
one complete wave cycle per second.
- Frequency = 1/(period in seconds)

Published under the
terms and conditions of the Design Science
License Disclaimer