AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
 

In article .com,
Keith Dysart wrote:

On Jul 16, 11:31 am, John Fields
wrote:
On Sun, 15 Jul 2007 14:57:17 -0700, Keith Dysart
wrote:
I thought the experiment being discussed was one where the
modulation was 1e5, the carrier 1e6 and the resulting
spectrum .9e6, 1e6 and 1.1e6.

---
That was my understanding, and is why I was surprised when you made
the claim, above:

"It does not matter how the .9e6, 1.0e6 and 1.1e6 are put into
the resulting signal. One can multiply 1e6 by 1e5 with a DC
offset, or one can add .9e6, 1.0e6 and 1.1e6. The resulting
signal is identical."

which I interpret to mean that three unrelated signals occupying
those spectral positions were identical to three signals occupying
the same spectral locations, but which were created by heterodyning.

Are you now saying that wasn't your claim?
---

No, that was indeed the claim. As a demonstration, I've
attached a variant of your original LTspice simulation.
Plot Vprod and Vsum. They are on top of each other.
Plot the FFT for each. They are indistinguishable.

-- lots o' snipping goin' on --

OK. I haven't been (had the patience to keep on) following this
discussion, so I apologize if this is totally inappropriate, but

If the statements above refer to creating that set of signals by using a
bunch of signal generators, or alternately by using some sort of actual
"modulation", the answer is, there is a very significant difference.

In the case where the set is created by modulating the "carrier" with
the low frequency, there is a very specific phase relationship between
the signals which would be essentially impossible to achieve if the
signals were to be generated independently. In fact, the only difference
between AM and FM/PM is that the phase relationship between the carrier
and the sideband set differs by 90 degrees between the two.

Isaac

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

Ron Baker, Pluralitas! wrote:
"isw" wrote:

After you get done talking about modulation and sidebands, somebody
might want to take a stab at explaining why, if you tune a receiver to
the second harmonic (or any other harmonic) of a modulated carrier (AM
or FM; makes no difference), the audio comes out sounding exactly as it
does if you tune to the fundamental? That is, while the second harmonic
of the carrier is twice the frequency of the fundamental, the sidebands
of the second harmonic are *not* located at twice the frequencies of the
sidebands of the fundamental, but rather precisely as far from the
second harmonic of the carrier as they are from the fundamental.

Isaac

Whoa. I thought you were smoking something but
my curiosity is piqued.
I tried shortwave stations and heard no harmonics.
But that could be blamed on propagation.
There is an AM station here at 1.21 MHz that is s9+20dB.
Tuned to 2.42 MHz. Nothing. Generally the lowest
harmonics should be strongest. Then I remembered
that many types of non-linearity favor odd harmonics.
Tuned to 3.63 MHz. Holy harmonics, batman.
There it was and the modulation was not multiplied!
Voices sounded normal pitch. When music was
played the pitch was the same on the original and
the harmonic.

One clue is that the effect comes and goes rather
abruptly. It seems to switch in and out rather
than fade in an out. Maybe the coming and going
is from switching the audio material source?

This is strange. If a signal is multiplied then the sidebands
should be multiplied too.
Maybe the carrier generator is generating a
harmonic and the harmonic is also being modulated
with the normal audio in the modulator.
But then that signal would have to make it through
the power amp and the antenna. Possible, but
why would it come and go?
Strange.

I've once listened to the first five harmonics of a
powerful medium wave transmitter (400 kW) at
a distance of some 300 m.
All harmonics gave normal audio; no strange
switching effects (Sony ICF-7600D).

What I'd like to know is if in such an 'experiment'
it can be excluded that (some of) these signals are
generated by the receiver itself.

gr, Hein

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

isw wrote:
"Ron Baker, Pluralitas!" wrote:

Then you understand Fourier transforms and convolution.

I suppose so; I've spent over fifteen years poking around in the
entrails of MPEG...

Ever learned, unfortunately seldom used.
What can radio hobbyists do with Fourier transforms
nowadays? (Nowadays, for aids and appliances like
software and spectrum analysers take over some work.)
If somebody could provide some examples I'd be grateful.
Thanks.

gr, Hein

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

John Fields wrote:
Hein ten Horn wrote:
John Fields wrote:

And what does it look like, then?

Roughly like the ones in your Excel(lent) plots. :)

I've posted nothing like that, so if you have graphics which support
your position I'm sure we'd all be happy to see them.

Oops, I'm sorry Keith!
http://keith.dysart.googlepages.com/radio5

Mathematical terms like linear, logarithmic, etc. are familiar
to me, but the guys here use linear and nonlinear in another
sense.

Retrospectively viewed: not the term "linear".

gr, Hein

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

"Ron Baker, Pluralitas!" wrote in message
...

"Hein ten Horn" wrote in message
...
Ron Baker, Pluralitas! wrote:
"Hein ten Horn" wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:

As a matter of fact the resulting force (the resultant) is
fully determining the change of the velocity (vector) of
the element.
The resulting force on our element is changing at the
frequency of 222 Hz, so the matter is vibrating at the
one and only 222 Hz.

Your idea of frequency is informal and leaves out
essential aspects of how physical systems work.

Nonsense. Mechanical oscillations are fully determined by
forces acting on the vibrating mass. Both mass and resulting force
determine the frequency. It's just a matter of applying the laws of
physics.

You don't know the laws of physics or how to apply them.

I'm not understood. So, back to basics.
Take a simple harmonic oscillation of a mass m, then
x(t) = A*sin(2*pi*f*t)
v(t) = d(x(t))/dt = 2*pi*f*A*cos(2*pi*f*t)
a(t) = d(v(t))/dt = -(2*pi*f)^2*A*sin(2*pi*f*t)
hence
a(t) = -(2*pi*f)^2*x(t)

Only for a single sinusoid.

and, applying Newton's second law,
Fres(t) = -m*(2*pi*f)^2*x(t)
or
f = ( -Fres(t) / m / x(t) )^0.5 / (2pi).

Only for a single sinusoid.
What if x(t) = sin(2pi f1 t) + sin(2pi f2 t)

In the following passage I wrote "a relatively
slow varying amplitude", which relates to the
4 Hz beat in the case under discussion (f1 =
220 Hz and f2 = 224 Hz) where your
expression evaluates to
x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t),
indicating the matter is vibrating at 222 Hz.

So where did you apply the laws of physics?
You said, "It's just a matter of applying the laws of
physics." Then you did that for the single sine case. Where
is your physics calculation for the two sine case?
Where is the expression for 'f' as in your first
example? Put x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t)
in your calculations and tell me what you get
for 'f'.

And how do you get 222 Hz out of
cos(2pi 2 t) * sin(2pi 222 t)
Why don't you say it is 2 Hz? What is your
law of physics here? Always pick the bigger
number? Always pick the frequency of the
second term? Always pick the frequency of
the sine?
What is "the frequency" of
cos(2pi 410 t) * cos(2pi 400 t)


What is "the frequency" of
cos(2pi 200 t) + cos(2pi 210 t) + cos(2pi 1200 t) + cos(2pi 1207 t)



So my statements above, in which we have
a relatively slow varying amplitude (4 Hz),

How do you determine amplitude?
What's the math (or physics) to derive
amplitude?

are fundamentally spoken valid.
Calling someone an idiot is a weak scientific argument.

Yes.
And so is "Nonsense." And so is your idea of
"the frequency".

Note the piquant difference: nonsense points
to content and we're not discussing idiots
(despite a passing by of some very strange
postings. :)).

Hard words break no bones, yet deflate creditability.

gr, Hein




Well, I think I've had it. A 'never' ending story.
Too much to straighten out. Too much comment
needed. Questions moving away from the subject.
No more indistinguishable close frequencies.
No audible beat, no slow changing envelopes.

Take a plot, use a high speed camera or whatever
else and see for yourself the particle is vibrating at a
period in accordance with 222 Hz. In my view I've
sufficiently underpinned the 222 Hz frequency.
If you disagree, then do the job. Show your
frequencies and elucidate them. (No hint needed,
I guess.)

gr, Hein

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

On Mon, 16 Jul 2007 12:28:07 -0700, Jim Kelley
wrote:

John Fields wrote:

On Fri, 06 Jul 2007 19:04:00 -0000, Jim Kelley
wrote:

In your example, with 300Hz and 400Hz as the carriers, the sidebands
would be located at:

f3 = f1 + f2 = 300Hz + 400Hz = 700Hz

and

f4 = f2 - f1 = 400Hz - 300Hz = 100Hz


both of which are clearly within the range of frequencies to which
the human ear responds.

Indeed. We would hear f3 and f4 if they were in fact there.

Your use of the term "beat frequency" is confusing since it's
usually used to describe the products of heterodyning, not the
audible warble caused by the vector addition of signals close to
unison.

The term is commonly used in describing the results of interference in
time, as well as for mixing.

Since the response of the ear is non-linear in amplitude it has no
choice _but_ to be a mixer and create sidebands.

Perhaps you're confusing log(sin(a)+sin(b)) with
log(sin(a))+log(sin(b)).

---
Perhaps, but I don't think either of those is correct, since for
mixing to occur (AIUI, for sidebands to be generated) the sine waves
themselves must be multiplied at the lowest level of the equation
instead of added.

That is, the solution of


log(sin(a)+sin(b))


will describe the numerical value of the logarithm of the vector sum
of two sine waves, and since the addition created no sidebands, the
output of the circuitry providing the logarithmic transfer function
will only be the instantaneous value of the logarithm of the vector
sum of the amplitudes of both signals.

Similarly,


log(sin(a))+log(sin(b))


describes the addition of the logarithm of the amplitude of sin(a)
to the logarithm of the amplitude of sin(b), which still produces
only a sum.

That is, no sidebands.
---

If you don't mind me asking, where did you get this notion about the
ears creating sidebands?

---
Well, whether I mind or not it seems you've asked anyway, so your
concern for my sensitivity is feigned.

That, coupled with your relegating it to being a "notion", seems to
be designed to discredit the hypothesis, offhandedly, and make me
work against a headwind in order to prove it valid, with you being
the negative authoritarian blowhard detractor.

If you're really interested in the subject I'll be happy to discuss
it with you if you can keep your end of the discussion objective and
free from pejorative comments.

Otherwise, **** off. ;^) -- Note tongue-in-cheek smiley, :-)


--
JF

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

In article ,
"Michael A. Terrell" wrote:

Hein ten Horn wrote:

I've once listened to the first five harmonics of a
powerful medium wave transmitter (400 kW) at
a distance of some 300 m.
All harmonics gave normal audio; no strange
switching effects (Sony ICF-7600D).

What I'd like to know is if in such an 'experiment'
it can be excluded that (some of) these signals are
generated by the receiver itself.


That much power that close to the receiver? Its a wonder you didn't
destroy the receiver's frontend.

That particular receiver doesn't have much of a "front end"; diodes
(with protection) and straight into the first mixer. No RF stage, tuned
or otherwise.

Isaac

AM electromagnetic waves: 20 KHz modulation frequency on anast...
 

But, can you ride electromagnetic waves? Will they astronomically
modulate you?
cuhulin

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-lowcarrier frequency
 

John Fields wrote:

log(sin(a))+log(sin(b))


describes the addition of the logarithm of the amplitude of sin(a)
to the logarithm of the amplitude of sin(b), which still produces
only a sum.

That is, no sidebands.

log(x)+log(y)=log(x*y)

jk

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

Michael A. Terrell wrote:
isw wrote:

That particular receiver doesn't have much of a "front end"; diodes
(with protection) and straight into the first mixer. No RF stage, tuned
or otherwise.

It can exceed the PIV of the protection diodes and cause them to
short, or explode. That crappy Sony design is where the harmonics came
from. The diodes, (or any other semiconductor) with enough RF can
generate a lot of spurious signals. It can even come from a rusty joint
in the area.

Is the ICF-SW7600GR significantly better performing
than the ICF-7600D on this?

gr, Hein

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

"Ron Baker, Pluralitas!" wrote in message news:469db833$0$20583
"Hein ten Horn" wrote in message
"Ron Baker, Pluralitas!" wrote in message
"Hein ten Horn" wrote in message
Ron Baker, Pluralitas! wrote:
"Hein ten Horn" wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:

As a matter of fact the resulting force (the resultant) is
fully determining the change of the velocity (vector) of
the element.
The resulting force on our element is changing at the
frequency of 222 Hz, so the matter is vibrating at the
one and only 222 Hz.

Your idea of frequency is informal and leaves out
essential aspects of how physical systems work.

Nonsense. Mechanical oscillations are fully determined by
forces acting on the vibrating mass. Both mass and resulting force
determine the frequency. It's just a matter of applying the laws of
physics.

You don't know the laws of physics or how to apply them.

I'm not understood. So, back to basics.
Take a simple harmonic oscillation of a mass m, then
x(t) = A*sin(2*pi*f*t)
v(t) = d(x(t))/dt = 2*pi*f*A*cos(2*pi*f*t)
a(t) = d(v(t))/dt = -(2*pi*f)^2*A*sin(2*pi*f*t)
hence
a(t) = -(2*pi*f)^2*x(t)

Only for a single sinusoid.

and, applying Newton's second law,
Fres(t) = -m*(2*pi*f)^2*x(t)
or
f = ( -Fres(t) / m / x(t) )^0.5 / (2pi).

Only for a single sinusoid.
What if x(t) = sin(2pi f1 t) + sin(2pi f2 t)

In the following passage I wrote "a relatively
slow varying amplitude", which relates to the
4 Hz beat in the case under discussion (f1 =
220 Hz and f2 = 224 Hz) where your
expression evaluates to
x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t),
indicating the matter is vibrating at 222 Hz.

So where did you apply the laws of physics?
You said, "It's just a matter of applying the laws of
physics." Then you did that for the single sine case. Where
is your physics calculation for the two sine case?
Where is the expression for 'f' as in your first
example? Put x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t)
in your calculations and tell me what you get
for 'f'.

And how do you get 222 Hz out of
cos(2pi 2 t) * sin(2pi 222 t)
Why don't you say it is 2 Hz? What is your
law of physics here? Always pick the bigger
number? Always pick the frequency of the
second term? Always pick the frequency of
the sine?
What is "the frequency" of
cos(2pi 410 t) * cos(2pi 400 t)


What is "the frequency" of
cos(2pi 200 t) + cos(2pi 210 t) + cos(2pi 1200 t) + cos(2pi 1207 t)



So my statements above, in which we have
a relatively slow varying amplitude (4 Hz),

How do you determine amplitude?
What's the math (or physics) to derive
amplitude?

are fundamentally spoken valid.
Calling someone an idiot is a weak scientific argument.

Yes.
And so is "Nonsense." And so is your idea of
"the frequency".

Note the piquant difference: nonsense points
to content and we're not discussing idiots
(despite a passing by of some very strange
postings. :)).

Hard words break no bones, yet deflate creditability.

Well, I think I've had it. A 'never' ending story.
Too much to straighten out. Too much comment
needed. Questions moving away from the subject.
No more indistinguishable close frequencies.
No audible beat, no slow changing envelopes.

Take a plot, use a high speed camera or whatever
else and see for yourself the particle is vibrating at a
period in accordance with 222 Hz. In my view I've
sufficiently underpinned the 222 Hz frequency.
If you disagree, then do the job. Show your
frequencies and elucidate them. (No hint needed,
I guess.)

Bravo. Well done. What an impressive
display of applying the laws of physics.
Newton, Euler, Gauss, and Fourier have nothing
on you.

Thanks for your constructive contributions.

gr, Hein

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

Jim Kelley wrote
Hein ten Horn wrote:

That's a misunderstanding.
A vibrating element here (such as a cubic micrometre
of matter) experiences different changing forces. Yet
the element cannot follow all of them at the same time.
As a matter of fact the resulting force (the resultant) is
fully determining the change of the velocity (vector) of
the element.

The resulting force on our element is changing at the
frequency of 222 Hz, so the matter is vibrating at the
one and only 222 Hz.

Under the stated conditions there is no sine wave oscillating at 222 Hz.
The wave has a complex shape and contains spectral components at two
distinct frequencies (neither of which is 222Hz).

Not a pure sine oscillation (rather than wave), but a near sine
oscillation at an exact period of 1/222 s. The closer the source
frequenties, the better the sine fits a pure sine. Thus if you
wish to get a sufficient near harmonic oscillation, conditions like
"slow changing envelope" are essential.

It might be correct to say that matter is vibrating at an
average, or effective frequency of 222 Hz.


No, it is correct. A particle cannot follow two different
harmonic oscillations (220 Hz and 224 Hz) at the same
time.

The particle also does not average the two frequencies.

Hmm, let's examine this.
From the two composing oscillations you get the overall
displacement:
y(t) = sin(2 pi 220 t) + sin(2 pi 224 t)
From the points of intersection of y(t) at the time-axes you
can find the period of the function, so examine when y(t) = 0.
sin(2 pi 220 t) + sin(2 pi 224 t) = 0
(..)
(Assuming you can do the math.)
(..)
The solutions a
t = k/(220+224) with k = 0, 1, 2, 3, etc.
so the time between two successive intersections is
Dt = 1/(220+224) s.
With two intersections per period, the period is
twice as large, thus
T = 2/(220+224) s,
hence the frequency is
f = (220+224)/2 = 222 Hz,
which is the arithmetic average of both composing
frequencies.

The waveform which results from the sum of two pure sine waves is not a pure
sine wave, and therefore cannot be accurately described at any single
frequency.

As seen above, the particle oscillates (or vibrates) at 222 Hz.
Since the oscillation is non-harmonic (not a pure sine),
it needs several harmonic oscillations (frequencies,
here 220 Hz and 224 Hz) to compose the oscillation at 222 Hz.

Obviously. It's a very simple matter to verify this by experiment.

Indeed, it is. But watch out for misinterpretations of
the measuring results! For example, if a spectrum
analyzer, being fed with the 222 Hz signal, shows
that the signal can be composed from a 220 Hz and
a 224 Hz signal, then that won't mean the matter is
actually vibrating at those frequencies.

:-) Matter would move in the same way the sound pressure wave does,

To be precise, this is nonsense, but I suspect you're trying
to state somewhat else, and since I'm not able to read your
mind today, I skip that part. :)

the amplitude of which is easily plotted versus time using Mathematica,
Mathcad, Sigma Plot, and even Excel. I think you should still give that a
try.

No peculiarities found.

gr, Hein

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-lowcarrier frequency
 

Hein ten Horn wrote:

Hmm, let's examine this.
From the two composing oscillations you get the overall
displacement:
y(t) = sin(2 pi 220 t) + sin(2 pi 224 t)
From the points of intersection of y(t) at the time-axes you
can find the period of the function, so examine when y(t) = 0.
sin(2 pi 220 t) + sin(2 pi 224 t) = 0
(..)
(Assuming you can do the math.)
(..)
The solutions a
t = k/(220+224) with k = 0, 1, 2, 3, etc.
so the time between two successive intersections is
Dt = 1/(220+224) s.
With two intersections per period, the period is
twice as large, thus
T = 2/(220+224) s,
hence the frequency is
f = (220+224)/2 = 222 Hz,
which is the arithmetic average of both composing
frequencies.

As I said before, it might be correct to say that the average, or
effective frequency is 222 Hz. But the actual period varies from
cycle to cycle over a period of 1/(224-220).

the amplitude of which is easily plotted versus time using Mathematica,
Mathcad, Sigma Plot, and even Excel. I think you should still give that a
try.


No peculiarities found.

Perhaps you would agree that a change in period of less than 2% might
be difficult to observe - especially when you're not expecting to see
it. To more easily find the 'peculiarities' I suggest that you try
using more widely spaced frequencies.

gr, Hein

gr right back at ya,

jk

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

How do you determine amplitude?
What's the math (or physics) to derive
amplitude?

The fundamental formular Acos(B) + C is all you need to describe angular
modulation.
Changing the value of A over time determines the amplitude of an AM
modulated carrier.
Changing the value of B over time determines the amplitude of an FM
modulated carrier.
The rate of change of A or B changes the modulation frequency respectively.
C is DC, Y axis offset and has not been discussed here.

r, Bob F.

AM electromagnetic waves: 20 KHz modulation frequency on anastronomically-low carrier frequency
 

Michael A. Terrell wrote:

I only have one portable receiver, the RS DX-375, which is kept in
my hurricane emergency kit. It was bought on price, alone...

I had one and was quite disappointed by its image response (even in
the absence of strong signal IMD, overloading, etc.). For example,
WWV on 10 Mhz was equally strong on 9545 kHz. I never saw the
schematic so I know nothing about its front end and evidently
it is single conversion but one would have hoped for a varactor
tuned preselector ;)

How is image rejection on yours?

Cross-posts limited to sci.electronics.basics and rec.radio.shortwave

Regards,

Michael

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

msg ) writes:
Michael A. Terrell wrote:

I only have one portable receiver, the RS DX-375, which is kept in
my hurricane emergency kit. It was bought on price, alone...

I had one and was quite disappointed by its image response (even in
the absence of strong signal IMD, overloading, etc.). For example,
WWV on 10 Mhz was equally strong on 9545 kHz. I never saw the
schematic so I know nothing about its front end and evidently
it is single conversion but one would have hoped for a varactor
tuned preselector ;)

It's completely unlikely that it doesn't have a tuned front end.
Because the whole notion of "tracking" came about when early on
it was realized that images were a bad side effect of the superheterodyne
receiver, and it they didn't set it up so the front end tuning
wasn't tuned with the same knob as the oscillator, it would be too easy
to mistune to the image.

The bad image rejection is a reflection of the low cost. Any cheap receiver
from forty years ago would likewise suffer bad image rejection. There really
is no real difference between a front end tuned with a mechanical
variable capacitor and a front end tuned with a varactor.

IN order to be cheap, such reacievers would skimp in the design. So there'd
be one or two tuned circuits before the mixer, and that wasn't enough
the higher you went in frequency with a 455KHz IF to get rid of the images.

On the other hand, a top end receiver like the HRO-60 was said to be pretty
good at image rejection, even getting up there close to 30MHz. The difference
was that it had more tuned circuits between the antenna and the mixer, so it
was far better able to reject the image.

Michael

AM electromagnetic waves: 20 KHz modulation frequency on anastronomically-low carrier frequency
 

msg wrote:

Michael A. Terrell wrote:

I only have one portable receiver, the RS DX-375, which is kept in
my hurricane emergency kit. It was bought on price, alone...

I had one and was quite disappointed by its image response (even in
the absence of strong signal IMD, overloading, etc.). For example,
WWV on 10 Mhz was equally strong on 9545 kHz. I never saw the
schematic so I know nothing about its front end and evidently
it is single conversion but one would have hoped for a varactor
tuned preselector ;)

How is image rejection on yours?


Its acceptable for emergency, but not what I'd want for daily use.
I have a 50 KW FM transmitter and multiple cell sites within a mile
Right now I'm restoring a 1950's era national NC183R with a properly
designed front end, with two tuned RF preamp stages.

http://bama.edebris.com/download/nat...c183/nc183.pdf See page 16
for the front end circuitry. (855 KB (876,468 bytes))


I also have a HP 312B frequency selective voltmeter:

http://bama.edebris.com/download/hp/312bd/hp312bd.pdf (106 MB download).


--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

Jim Kelley wrote:
Hein ten Horn wrote:

Hmm, let's examine this.
From the two composing oscillations you get the overall
displacement:
y(t) = sin(2 pi 220 t) + sin(2 pi 224 t)
From the points of intersection of y(t) at the time-axes you
can find the period of the function, so examine when y(t) = 0.
sin(2 pi 220 t) + sin(2 pi 224 t) = 0
(..)
(Assuming you can do the math.)
(..)
The solutions a
t = k/(220+224) with k = 0, 1, 2, 3, etc.
so the time between two successive intersections is
Dt = 1/(220+224) s.
With two intersections per period, the period is
twice as large, thus
T = 2/(220+224) s,
hence the frequency is
f = (220+224)/2 = 222 Hz,
which is the arithmetic average of both composing
frequencies.

As I said before, it might be correct to say that the average, or effective
frequency is 222 Hz. But the actual period varies from cycle to cycle over
a period of 1/(224-220).

the amplitude of which is easily plotted versus time using Mathematica,
Mathcad, Sigma Plot, and even Excel. I think you should still give that a
try.


No peculiarities found.

Perhaps you would agree that a change in period of less than 2% might be
difficult to observe - especially when you're not expecting to see it. To
more easily find the 'peculiarities' I suggest that you try using more
widely spaced frequencies.

Before we go any further I'd like to exclude
that we are talking at cross-purposes.
Are you pointing at the irregularities which
can occur when the envelope passes zero?
(That phenomenon has already been
mentioned in this thread.)


gr right back at ya,

:-)
"gr" is not customary, but, when writing it satisfies
in several languages: German (gruß, grüße),
Dutch (groet, groeten) and English.

Adieu, Hein