Jenjerina provides some key definitions in the comment below. More
specifics are perhaps best described in terms of some examples.
Starting with a musical example, consider a musical instrument such as
a violin. (Similar arguments can be made about many other
instruments.) Suppose the player plays middle-C. There are indeed
harmonics of this note with frequencies which are multiples of it.
Twice the frequency (the "second" harmonic; conventional harmonic
counting begins with the fundamental as number "one"!) is an octave
higher (C again). Three times the frequency is an octave and a fifth
higher (G). Four times the frequency is two octaves up. The fifth
harmonic is two octaves and a fourth up (F). The sixth is an octave (2
times) above the third (G again). The seventh harmonic is the first
one which is not a "perfect" interval (see
https://answers.google.com/answers/main?cmd=threadview&id=16918). The
eight harmonic is, of course, three octaves above the fundamental. How
many of these harmonics are important? That depends on a number of
factors. A harmonic is typically important if it reinforces something.
That can be a natural "resonance" such as some feature of the body of
the violin which tends to vibrate at that frequency. If there happens
to be such a resonance it will be "reinforced"; i.e., there will tend
to be energy transferred to that vibration mode. Such resonances
contribute to the "timbre" or characteristic sound of a musical
instrument. A reinforcement may also occur if two notes played at the
same time have at least some matching harmonics. For example, a
perfect fifth (two notes with a frequency ratio of 3/2) is a
"pleasing" interval, because the second harmonic of the upper note
matches the third harmonic of the lower note. In general, these
effects tend to be more important if the match is closer and involves
lower harmonics. In most cases, there is decreasing energy (amplitude)
in higher harmonics quite aside from any decreasing sensitivity of the
human ear as you go to higher frequencies. Note also that the
fundamental sound generation mechanism of most instruments actually
generates energy in harmonics as well as in the fundamental. Again,
taking the violin example, a vibrating string is easily excited in
harmonics as well as at the fundamental, because the string itself has
resonances at the harmonics. Typically (but not always), the player
tries to excite primarily the fundamental. Wind instruments derive
their distinctive sounds in large part from particular patterns of
harmonics which are excited simultaneously with the fundamental. Some
instruments such as the viola d'amore actually have a special set of
"sympathetic" strings which are not excited directly by plucking or
bowing but are simply there to resonate when the main strings are
played. The characteristic sound of a piano is influenced by the
sympathetic vibration of strings other than the ones actively being
struck as well.
Harmonics are important in the analysis and management of other sorts
of sound as well. Similar kinds of reinforcement may occur at
harmonics of noise sources, for example. Your lawn mower could excite
a resonance in your china cabinet. The cartoon image of an opera
singer's high note causing a glass to break is due to the same sort of
effect. (The effect is real if not nearly as common as the cartoon
image might indicate.)
Musical examples of harmonics and resonance effects may be among the
easier examples to grasp, but the same principles apply to vibrations
of any sort. The vibrating bridge example is a good one. Quartz
crystal oscillators depend on certain resonances in precision-cut
quartz crystals. Even atomic clocks depend on the same effect in the
electrons of certain atoms. Many of the properties of molecules depend
on the vibration properties of their constituent atoms.
Light is also a form of vibration. Electromagnetic waves are light.
Some light sources such as lasers tend to behave similarly to musical
instruments in that they tend to naturally "vibrate" (emit light) at a
characteristic frequency (color). The length of a laser "cavity"
corresponds to the length of a violin string or the length of an organ
pipe. Many such devices will also emit some light at harmonics of the
fundamental frequency. Since the visible spectrum is only about an
"octave," such harmonics tend not to be very important for the human
perception of light. However, they can be very important in certain
commercial lasers. There are special tricks that allow the doubling or
tripling of the fundamental of certain lasers (i.e., most of the light
energy is excited only in the second or third harmonic rather than the
fundamental). For example, a Nd-YAG laser typically wants to emit
infrared light at 1064 nm, but it can readily be excited at 532 nm
(green) by frequency doubling tricks. An analogy to the timbre effects
in musical instruments does exist for light in the form of the "color"
of objects. Normal "white" light actually contains a broad spectrum of
light (analogous to "white" noise--noise which does not have any
distinct identifiable pitch). When such light is reflected off a
surface, some colors are absorbed or reflected differently from others
as the light interacts with the molecules of the surface. The light
actually couples with electrons in the atoms. The frequency of visible
light may be much higher than that of audible sound, but when you get
to atomic scales, the vibration frequencies of individual atoms and
electrons can actually match those of visible photons.
A direct connection between "light" and "sound" is possible but of
minor importance in most cases, simply because the frequency ranges of
interest are usually so far apart that there is usually very little
energy coupled between them. Extending into "ultrasound" and "radio"
waves doesn't get you much closer in most applications. Most common
couplings between light and sound are more indirect. Some processes
generate both light and sound by different mechanisms (lightning and
thunder, for example). Similarly light can generate sound if enough of
it is absorbed into something to cause it to break or explode thereby
generating vibrations which are emitted as sound.
Obviously, the subject of vibrations, harmonics, resonances, light and
sound covers a lot of territory. I hope these few paragraphs gave you
a reasonable layman's introduction. If there are specific things which
are of particular interest to you, please request a clarification I'd
be happy to expand the discussion. Or if you really have a very
specific problem in mind, perhaps you can explain it, and I can help
you figure out what question you are really trying to ask.
And if you need some links to further reading in particular areas,
please ask for them as well. The above discussion was based on
personal knowledge, but I can easily refer you to textbooks or web
sites for more details on particular topics. |
Request for Answer Clarification by
jat-ga
on
03 Oct 2002 10:37 PDT
Thanks. Your comments are helpful. But, to further clarify, I'm
looking for a relationship between the higher, EMF frequencies and the
lower frequencies we call "sound" (including ultra-sound). I notice
that you don't normally see the "sound" frequencies listed on a
spectrum chart of the other frequencies. I realize they are far apart
as to their actual frequency ranges, but I'm still wondering if there
still exists some kind of continuity between them. They are, after
all, frequencies. An earlier piece of input I received made the
distinction that soundwaves are different, since they are "compression
frequencies", requiring a "medium". What I'm wondering, though, is
something more like taking a violin string and plucking it in a
vacuum. No sound is generated, but I assume it will vibrate with
almost exactly the same "frequency" that it would when we hear the
"compression waves" it generates when plucked in a normal atmospheric
environment. So, if it vibrates in a vacuum, then how is it any
different than, say, an antenna "vibrating" off a radio wave except
for the fact that its vibration is much slower? If I'm thinking
straight here, then it seems there would be a basis for maintaining
that all frequencies are "related", whether they be sound or light,
and therefore, harmonics can exist between sound frequencies and light
frequencies. Hope this helps to clarify what I've got in mind...
|
Clarification of Answer by
drdavid-ga
on
03 Oct 2002 16:11 PDT
As pointed out in the previous question you refer to:
https://answers.google.com/answers/main?cmd=threadview&id=70246
there are in fact named radio bands corresponding to audio and
ultrasonic frequencies. The word "frequency" refers to the repetition
rate of any oscillation or repetitive event whether it is compression
waves in air or in a wood block, transverse vibrations of a violin
string, the oscillation of an electromagnetic wave, the swaying of a
bridge, the swinging of a pendulum, or the number of people walking
past the corner of 5th Street and 7th Avenue. So, yes, you can put all
these frequencies on the same chart if you wish to. It is interesting
to note, for example, that certain relatively less familiar forms of
electromagnetic waves do, in fact, have the same frequencies as
audible sound and ultrasound, but they still represent different kinds
of vibration. And, yes, a violin string can still vibrate in a vacuum,
since the characteristics of a string which allow it to vibrate do not
depend on the presence of air. However, without the air, no vibrations
(sound) can be transmitted, say, to a microphone mounted even a few
inches away (assuming that it is isolated from any possible sound
transmission through the mounting hardware--remember that sound can
travel through solids as well as gases).
Whether vibrations of one sort couple in any significant way to
vibrations of another sort is not directly dependent on the frequency
of the vibration, but rather on whether there is a coupling mechanism.
If there is a coupling mechanism, and especially if there happen to be
resonances in the secondary medium which match the driving frequency
from the first medium, then important coupling can indeed occur. The
Tacoma Narrows bridge failure is a classic example. There are also
examples of similar failures when soldiers marched in step across some
structure or many people at a disco were all moving synchronously.
There are also ways that sound and light can couple, but they are
relatively unusual situations, since the coupling mechanisms are
relatively rare and the frequency ranges of interest are usually far
apart. Even the ones that seem like good examples usually turn out to
be not a direct coupling of the underlying vibration. For example,
fluorescent lights tend to "hum," but not at the light frequency. They
hum because there is a superimposed fluctuation of the light
"intensity" driven by a vibrating electrical input. Such
superpositions of frequencies--one higher-frequency vibration
modulated at a much lower frequency (either the amplitude or the
frequency can be modulated)--are actually very common. Radio and TV
transmissions also do this by superimposing the information (for
example, musical sound or speech) as a low frequency modulation of a
"carrier" electromagnetic wave.
I hope that helps clear up your confusion.
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