Frequency Beats

Hi Wallyesterpaulrus,

Please see tuning message number 41866. You were comparing 105Hz to
100Hz which resulted in 5 frequency beats per second (105 – 100 = 5)

Also please reference your chart.

/tuning-math/files/Paul/walter.jpg

I studied this chart for quite some time but got side tracked. I
wanted to ask you a question regarding the actual frequency beats in
your chart.

You explained to me in message 41866…..

>at first, the green and blue waves are in phase, so the resultant
>(sum), the red wave, is similar in frequency but with twice the
>amplitude of either.

>after 1/10 of a second, the green and blue waves are out of phase,
so
>the so the resultant (sum) stays close to zero -- there's almost no
>amplitude, so basically silence, at this point in time.

>after 1/5 of a second, the green and blue waves are back in phase,
so
>you're back to maximum amplitude.

This I understand . At 1/10 of a second, both frequencies are out of
phase by 180 degrees therefore there is almost no amplitude.

However when I mentally extended the chart from your original time
frame of 1/5 of a second to 1 second, I was able to visualize 5
separate times when the amplitude was at it's highest to lowest and
then back to highest.

But I did not actual see 5 complete cycles per second. In other
words, each 1/5 of a second contained only a half cycle starting with
the highest amplitude (90 degrees) to the lowest amplitude (180
degrees) and then back to highest amplitude (270 degrees).

One complete cycle (or beat) per 1/5 of a second is defined as
amplitude variation from 0 degrees through and including 360 degrees
(5Hz = 5 "complete" cycles per second). Correct? Yet the chart is
starting at 90 degrees and stopping at 270 degrees which is ½ cycle.
Correct? Or what am I doing wrong?

Can you please extend your chart out in time to 1 second so I can
actually see "5" complete cycles or beats per second?

Thank you
Walter

--- In tuning@yahoogroups.com, "Walter Lepore" <earth7@o...> wrote:
> Hi Wallyesterpaulrus,
>
> Please see tuning message number 41866. You were comparing 105Hz to
> 100Hz which resulted in 5 frequency beats per second (105 – 100 = 5)
>
> Also please reference your chart.
>
> /tuning-math/files/Paul/walter.jpg
>
> I studied this chart for quite some time but got side tracked. I
> wanted to ask you a question regarding the actual frequency beats
in
> your chart.
>
> You explained to me in message 41866…..
>
> >at first, the green and blue waves are in phase, so the resultant
> >(sum), the red wave, is similar in frequency but with twice the
> >amplitude of either.
>
> >after 1/10 of a second, the green and blue waves are out of phase,
> so
> >the so the resultant (sum) stays close to zero -- there's almost
no
> >amplitude, so basically silence, at this point in time.
>
> >after 1/5 of a second, the green and blue waves are back in phase,
> so
> >you're back to maximum amplitude.
>
> This I understand . At 1/10 of a second, both frequencies are out
of
> phase by 180 degrees therefore there is almost no amplitude.
>
> However when I mentally extended the chart from your original time
> frame of 1/5 of a second to 1 second, I was able to visualize 5
> separate times when the amplitude was at it's highest to lowest and
> then back to highest.
>
> But I did not actual see 5 complete cycles per second. In other
> words, each 1/5 of a second contained only a half cycle starting
with
> the highest amplitude (90 degrees) to the lowest amplitude (180
> degrees) and then back to highest amplitude (270 degrees).

walter, perhaps you're confusing amplitude cycles with pressure or
displacement cycles. amplitude cannot be negative. therefore a
complete amplitude cycle has occured when you've gone from the
highest amplitude to the lowest amplitude (zero) and back to the
highest amplitude. there's nowhere else you can go, and this pattern
will simply repeat itself in time -- there's no missing half-cycle.

> One complete cycle (or beat) per 1/5 of a second is defined as
> amplitude variation from 0 degrees through and including 360
degrees
> (5Hz = 5 "complete" cycles per second). Correct? Yet the chart is
> starting at 90 degrees and stopping at 270 degrees which is ½
cycle.
> Correct?

nope, it's a full beat -- you'll hear five points of maximum
amplitude, and hence 5 beats, every second. it's as simple as that!

> Can you please extend your chart out in time to 1 second so I can
> actually see "5" complete cycles or beats per second?

just paste 5 copies of the chart end-to-end! the pattern simply
repeats itself.

Hi Paul and all Tuning Members

> walter, perhaps you're confusing amplitude cycles with pressure or
> displacement cycles. amplitude cannot be negative.

Yes! That was indeed my problem. I can't believe I fell into that
trap!

>> Can you please extend your chart out in time to 1 second so I can
>> actually see "5" complete cycles or beats per second?

>just paste 5 copies of the chart end-to-end! the pattern simply
> repeats itself.

Paul, I emailed you a chart . I created it in "Paint Brush". It's
a .bmp file. I did not know how to upload it to this message.

Please follow me on this response to make sure I've got it right.

In other words, the difference between the two component frequencies
in your earlier example is 5Hz (105Hz – 100Hz). This 5Hz is
NOT "Pressure Cycles" which indicates the "pitch of a particular
frequency" but is known as "Amplitude Cycles" which indicates
the "volume fluctuation" of a particular frequency.

I was defining the difference of 5Hz as the "frequency 5Hz" which
is "below" the threshold of hearing (20Hz to 20,000HZ). One must be
careful when defining 5Hz due to the fact that 5Hz can be defined in
numerous ways depending on the context to which it is being used.
5Hz can be defined as "Pressure Frequency" or "Amplitude Frequency"

Therefore the term "Hz" (Hertz) which in itself is defined,
as "cycles per second" can be associated with either AMPLITUDE CYCLES
PER SECOND or PRESSURE CYCLES PER SECOND.

One Amplitude Waveform Cycle travels from positive to zero to
positive. The vertical axis in an Amplitude Variation Chart is a
measurement of amplitude (or decibels), starting at zero and moving
in a positive direction of increasing amplitude.

One "Amplitude Cycle" begins when……..
A)The composite waveform is at its highest amplitude ("x" decibels)
B)The waveform descends to the lowest amplitude (zero decibels)
C)The waveform climbs back up to its highest amplitude ("x" decibels)
Each beat is one point of maximum amplitude

One "Pressure Waveform Cycle" travels from 0 degrees through and
including 360 degrees. The vertical axis in a pressure chart is a
scale of positive, neutral (0) and negative pressure.

One "Pressure Cycle" begins when….
A)The air molecules are at a state of maximum equilibrium (0 degrees)
B)The air molecules continue to be compressed until they are at a
positive state of maximum compression (90 degrees)
C)The air molecules then begin to decompress and return to a
momentary state of maximum equilibrium (180 degrees)
D)The air molecules then move on to a negative state of maximum
rarefaction (270 degrees)
E)The air molecules then return to a state of maximum equilibrium
(360 degrees).

As a result of the two components frequencies (105Hz and 100Hz) being
of "different" frequencies, a composite waveform is created which is
about 102.5Hz.

This 102.5Hz is defined as the resulting "pitch frequency" or
as "102.5 Composite Waveform Cycles" of Pressure Per Second".

The difference of 5Hz (105Hz and 100Hz) is defined as "the frequency
of interference beats" or as "5 Cycles of Amplitude Variation Per
Second".

Correct (I hope)?

Thank you for your patience
Walter

--- In tuning@yahoogroups.com, "Walter Lepore" <earth7@o...> wrote:
> Hi Paul and all Tuning Members
>
> > walter, perhaps you're confusing amplitude cycles with pressure
or
> > displacement cycles. amplitude cannot be negative.
>
> Yes! That was indeed my problem. I can't believe I fell into that
> trap!
>
> >> Can you please extend your chart out in time to 1 second so I
can
> >> actually see "5" complete cycles or beats per second?
>
> >just paste 5 copies of the chart end-to-end! the pattern simply
> > repeats itself.
>
> Paul, I emailed you a chart . I created it in "Paint Brush". It's
> a .bmp file. I did not know how to upload it to this message.
>
> Please follow me on this response to make sure I've got it right.
>
> In other words, the difference between the two component
frequencies
> in your earlier example is 5Hz (105Hz – 100Hz). This 5Hz is
> NOT "Pressure Cycles" which indicates the "pitch of a particular
> frequency" but is known as "Amplitude Cycles" which indicates
> the "volume fluctuation" of a particular frequency.
>
> I was defining the difference of 5Hz as the "frequency 5Hz" which
> is "below" the threshold of hearing (20Hz to 20,000HZ). One must
be
> careful when defining 5Hz due to the fact that 5Hz can be defined
in
> numerous ways depending on the context to which it is being used.
> 5Hz can be defined as "Pressure Frequency" or "Amplitude Frequency"
>
> Therefore the term "Hz" (Hertz) which in itself is defined,
> as "cycles per second" can be associated with either AMPLITUDE
CYCLES
> PER SECOND or PRESSURE CYCLES PER SECOND.
>
> One Amplitude Waveform Cycle travels from positive to zero to
> positive. The vertical axis in an Amplitude Variation Chart is a
> measurement of amplitude (or decibels), starting at zero and moving
> in a positive direction of increasing amplitude.
>
> One "Amplitude Cycle" begins when……..
> A)The composite waveform is at its highest amplitude ("x" decibels)
> B)The waveform descends to the lowest amplitude (zero decibels)
> C)The waveform climbs back up to its highest amplitude ("x"
decibels)
> Each beat is one point of maximum amplitude
>
>
> One "Pressure Waveform Cycle" travels from 0 degrees through and
> including 360 degrees. The vertical axis in a pressure chart is a
> scale of positive, neutral (0) and negative pressure.
>
> One "Pressure Cycle" begins when….
> A)The air molecules are at a state of maximum equilibrium (0
degrees)
> B)The air molecules continue to be compressed until they are at a
> positive state of maximum compression (90 degrees)
> C)The air molecules then begin to decompress and return to a
> momentary state of maximum equilibrium (180 degrees)
> D)The air molecules then move on to a negative state of maximum
> rarefaction (270 degrees)
> E)The air molecules then return to a state of maximum equilibrium
> (360 degrees).
>
> As a result of the two components frequencies (105Hz and 100Hz)
being
> of "different" frequencies, a composite waveform is created which
is
> about 102.5Hz.
>
> This 102.5Hz is defined as the resulting "pitch frequency" or
> as "102.5 Composite Waveform Cycles" of Pressure Per Second".
>
> The difference of 5Hz (105Hz and 100Hz) is defined as "the
frequency
> of interference beats" or as "5 Cycles of Amplitude Variation Per
> Second".
>
> Correct (I hope)?

you get an a+!

Hi Paul and tuning members,

This is a corrected version of message # 43164.

> walter, perhaps you're confusing amplitude cycles with pressure or
> displacement cycles. amplitude cannot be negative.

Yes! That was indeed my problem. I can't believe I fell into that
trap!

>> Can you please extend your chart out in time to 1 second so I can
>> actually see "5" complete cycles or beats per second?

>just paste 5 copies of the chart end-to-end! the pattern simply
> repeats itself.

Paul, I emailed you a chart . I created the chart in "Paint Brush".
It's a .bmp file. I realized .bmp files cannot be uploaded to the
tuning list.

Please follow me on this response to make sure I've got it right.

In other words, the difference between the two component frequencies
in your earlier example is 5Hz (105Hz – 100Hz). This 5Hz is
NOT "Pressure Cycles" which indicates the "pitch of a particular
frequency" but is known as "Amplitude Cycles" which indicates
the "volume fluctuation" of a particular frequency.

I was defining the difference of 5Hz as "5 cycles per second of
pressure frequency". Which of course would be a frequency "below" the
threshold of hearing (20Hz to 20,000HZ). One must be careful when
defining 5Hz due to the fact that 5Hz can be defined in numerous ways
depending on the context to which it is being used.
5Hz can be defined as "Pressure Frequency" or "Amplitude Frequency"

Therefore the term "Hz" (Hertz) which in itself is defined,
as "cycles per second" can be associated with either AMPLITUDE CYCLES
PER SECOND or PRESSURE CYCLES PER SECOND.

One Amplitude Waveform Cycle travels from positive to zero to
positive. The vertical axis in an Amplitude Variation Chart is a
measurement of amplitude (or decibels), starting at zero and moving
in a positive direction of increasing amplitude.

One "Amplitude Cycle" begins when……..
A)The composite waveform is at its highest amplitude ("x" decibels)
B)The waveform descends to the lowest amplitude (zero decibels)
C)The waveform climbs back up to its highest amplitude ("x" decibels)
Each beat is one point of maximum amplitude

One "Pressure Waveform Cycle" travels from 0 degrees through and
including 360 degrees. The vertical axis in a pressure chart is a
scale of positive, neutral (0) and negative pressure.

One "Pressure Cycle" begins when….
A)The air molecules are at a state of maximum equilibrium (0 degrees)
B)The air molecules continue to be compressed until they are at a
positive state of maximum compression (90 degrees)
C)The air molecules then begin to decompress and return to a
momentary state of maximum equilibrium (180 degrees)
D)The air molecules then move on to a negative state of maximum
rarefaction (270 degrees)
E)The air molecules then return to a state of maximum equilibrium
(360 degrees).

As a result of the two components frequencies (105Hz and 100Hz) being
of "different" frequencies, a composite waveform is created which is
about 102.5Hz.

This 102.5Hz is defined as the resulting "pitch frequency" or
as "102.5 Composite Waveform Cycles" of Pressure Per Second".

The difference of 5Hz (105Hz and 100Hz) is defined as "the frequency
of interference beats" or as "5 Cycles of Amplitude Variation Per
Second".

Correct (I hope)?

Thank you for your patience
Walter

Hi Paul

> > Correct (I hope)?
>
> you get an a+!

Thank you. This stuff is finally starting to "click"!

Walter