Black hole music thread in other forum

[marcus]

LPF, you suggested starting a thread on BH ringing modes
and/or natural units.
I started a thread in "Stellar Astrophysics" forum

 

[8LPF16]

Marcus,

The thread starter you left brings up first question:

Is this Stellar Astrophysics, or LQG, or??

Other questions:

1. Can you use degrees instead of radians?

2. The closest I come to 1855 (A440tun.) is at 1864, which is an A#.
Where is the discrepancy?

Yes, I would like to know the more precise version of "Sun's mass/5 = 2 octaves".


LPF

 

[marcus]

Originally posted by 8LPF16
Marcus,


Yes, I would like to know the more precise version of "Sun's mass/5 = 2 octaves".


LPF

You like numbers and precision. So let's be more precise and you do some of the calculation. One thing at a time though :)

You know what the Planck mass unit is, in kilograms (its at the NIST site)
and suppose I tell you the sun's mass in kilograms. (having just checked in a couple of handbooks)
1.99 x 10³⁰ kilograms.

would you be willing to get us the sun's mass in Planck units?

 

[8LPF16]

Marcus,

I was hoping for a few Q & A's before testing but...

If this question is "elementary", then I give 9.1433e37. If it needs conversion, then I am not there yet.

(my next series of questions included Planck units)


Every once and a while, my location provides splendor of high order.
This morning, as I attempted this answer, the Moon set into a band of magenta and peach behind the snow capped Mission Mountains to my right. Moments later, the Sun's rays scattered blues and yellow so white they lose individuality, through the trees of "the Bob" to my left. Normally, my desk is rather boring!


LPF

 

[marcus]

Originally posted by 8LPF16
Marcus,

I was hoping for a few Q & A's before testing but...

If this question is "elementary", then I give 9.1433e37. If it needs conversion, then I am not there yet.

(my next series of questions included Planck units)


Every once and a while, my location provides splendor of high order.
This morning, as I attempted this answer, the Moon set into a band of magenta and peach behind the snow capped Mission Mountains to my right. Moments later, the Sun's rays scattered blues and yellow so white they lose individuality, through the trees of "the Bob" to my left. Normally, my desk is rather boring!


LPF

fantastic scenery! where are the Mission Mountains?

I am happy with M = 9.1433e37

Do you want to do the next step as well? You asked about a more accurate value of the frequency (and consequently the pitch) of a solar mass BH. this is (one way) how to get it.


plug that M into the formula

$$\frac{log3}{8\pi M}$$

the log is the natural logarithm, sometimes people write it "ln" for "log natural", and reserve "log" for base-10. Does your calculator have a "ln" key? Or anyhow, can you calculate this.

It will give the frequency and we can then find out how many octaves and musical halfsteps it is from middle D.

 

[8LPF16]

Marcus,

1. (on roads) 3 hrs. S of Glacier Ntl. Park & 4 hrs. NW of Yellowstone.

2. 4.78080e-40 ?

(I should get one question answered with every correct response!)


LPF

 

[marcus]

Originally posted by 8LPF16


4.78080e-40 ?

South of Glacier and NW of Yellowstone sounds like
living among the splendors of nature
I live among city lights and can't even see the stars at night, or not really well. the night sky is the umbilical for all the worthwhile thinking in the past 2500 years, I sometimes imagine, and we urbanites are cut off from it.

Well I'm happy with your 4.78e-40
-----------------------------------

Now I will calculate what A440 is, in Planck terms, and you can calculate the ratio.

there are two conventional formats for frequency and when using hbar (to relate freq to energy) one always uses angular
this is puzzling when first encountered and I'm not sure I know how to help someone over it. angular format just works efficiently and has been used for over 100 years.

all frequency is counting events per unit time
and with a vibration the event can either be a CYCLE or it
can be passage thru a radian of phase. or turning by a radian of angle, if the oscillation is actually a rotation. it has been
found efficient (leading to clean formulas) over the course of a long time by many physicists to deal with frequency in the latter way.
what can I say? there are two conventions and the Planck units that NIST lists and almost everybody thinks of as the Planck units are based on hbar.

if we want to go to cyclic freq format then we need to change from hbar to h in all the formulas and we get different Planck units and we confuse all the people who are used to these ones

likewise if we take a totally new tack and define the event to be counted as "passage thru one degree of phase" that is 1/360 of a cycle. One could measure freq that way but it would mean changing all the formulas.

so even tho it is unintuitive and seemingly arbitrary I am going to say that A is 880 pi per second.

NIST says Planck time is 5.39121e-44 second

So I multiply the two and get that standard A is
1.490455e-40

Let's round that off a bit and call it 1.49e-40

Pythagoreans should not be surprised because I told you earlier that D was e-40
and A is a major fifth up from D ("do" up to "sol")
so you would expect it to be a higher freq by a factor of 1.5

the fact that it is 1.49 is just because the customary A440 is not
exactly Planck. But actually the existing symphony orchestras each use their own tuning. Nobody really uses exactly A440, or so I have read. there is always some variation. So someday there may be an orchestra that uses Planck tuning either accidentally or intentionally. this doesn't matter. only that I do not take the number 440, or (in angular format) 880pi, too seriously.
-----------------------------------

so now we have the pitch middle A is 1.49e-40

and we have your number 4.78e-40
for the solar mass black hole pitch

what is the ratio (by what factor is the BH pitch higher than A?)

 

[marcus]

LPF,

I am trying to respond to your questions as we go along.
Has anything been left out so far?

Your number is 4.78e-40
and official A in music is 1.49e-40

so please get their ratio so we can find out how many musical steps your frequency is above official A.
---------------------------

commentary:
what this is really about is appreciating the universe's intrinsic frequency which on the scale we are using is unity-----one.

It is a very high frequency.

Try to grasp it.

More and more people seem to think that Planck energy
is an intrinsic thing built into spacetime where new physics
begins to happen---something meaningful like the speed of light.

But to every quantity of energy E
there corresponds a frequency omega
such that E = hbar omega
(sort of core fact of quantum mechanics
energy steps correspond to frequency steps)

So since there is this intrinsic absolute quantity of energy
there is also an intrinsic frequency----the universe has a pitch

but it is very high
so that middle D (which I know because I can sing it) is e-40
on a scale where the universe frequency is 1.
--------------

however this commentary is not what matters
It seems to me what matters right now is to get the
ratio, if you would please indulge me in this I would
appreciate it.

then we will interpret the ratio as musical steps

 

[8LPF16]

Marcus,


Before we play any further, we need to get in tune.

It is not surprising that expressing this idea is easier (more convenient) in terms of rotation, nor counterintuitive. The model that takes this form is the only way to go. I am just not used to seeing "radian" tuning. Can you give me a way to translate? I know that a radian is 57.3, but I can't remeber the total "radians per rotation". (I know the formula uses pi in 4 increments)


LPF


ps. In my mind, 360 is good for the total, or "potentials" of angular movement, for determining frequency change one degree at a time. However, I feel that 57.3 is too large to accurately describe the resonant interval, so I worked out my own. One interval "period" is 27.6923, which is derived from the fixed number representing the interval: 13 (half steps) What do you think of that?

 

[marcus]

2pi radians make a full cyle

 

[8LPF16]

Marcus,

Okay, so the whole cycle is 360.0265...

Does this give it 57.3 intervals of 2pi increments?

LPF

 

[marcus]

The circumference of a circle is 2pi R.
A radian sector of a circle is like you take a radius of the circle made of rubber and bend it along the circumference.
(it covers 57 some degrees, the exact number of degrees is not too imporatant)
2pi radians make a full circumference.

-----------
conventions can be frustrating and irritating
I sympathize. It would be nice if we could make up our own language for describing rates of rotation and rates of oscillation

in physics classes up thru sophomore year the predominant format is cyclic

then (because it makes the formulas simpler or because nature seems to prefer it or something, maybe sheer irrationality) they gradually switch over more to angular format

so in UPPER DIVISION undergrad courses, and even more in the graduate courses, you see the symbol omega for frequency, which is your clue to the fact that every complete cycle or compete rotation is counted as 2pi.

Something real ordinary like A440 belongs to the lower division undergrad curriculum. So the frequency of A would always be
called
f = 440 cycles per second = 440 Hz.
but the frequency of a black hole is upperdivision or grad, so it
would be called
ω = 880 pi radians per second = 2765 per second.
doesnt that seem ridiculous?
----------------

There is a fracture in physicists language.
When you read a textbook you have to be alert and watch whether he
is using the symbol f
or the symbol omega
for frequency

If you see ω then one full turn is 2pi.
It is actually convenient in a lot of cases, like if there is a wheel turning with frequency ω
then the speed of a bug sitting on the rim is ωR
where R is the radius of the wheel.

Or if you are on a merrygoround turning at rate ω
then how fast you go is ωR
where R is your distance out from the axle of the merrygoround.

and your acceleration towards center, which feels like "centrifugal force" to you, is
ω²R

Angular format is the format that makes it easy to calculate what they usually want to calculate.

but it is hard to explain it to Freshmen and hard to get the
Engineering majors to accept it. So they hold off and introduce it later in the curriculum after the Engineer majors have left.

And then you see more and more of hbar
and less and less of h
because hbar goes with angular format
E = hbar ω

dont blame me. human language has lots of absurdities
this little inconsistency of physicists frequency-language is
comparatively harmless---a mere pecadillo.

 

[marcus]

the number 57.3 you mentioned is only an approximation

if you want a better approximation of the degrees in a radian
then take 360 and divide by 2pi

that is the same as taking 180 and dividing by pi

 

[marcus]

I think you have been admirably patient and that I should
finish the problem up

 

[marcus]

Originally posted by marcus
...

Well I'm happy with your 4.78e-40
-----------------------------------

Now I will calculate what A440 is, in Planck terms, and you can get the calculate the ratio.

...
-----------------------------------

so now we have the pitch middle A is 1.49e-40

and we have your number 4.78e-40
for the solar mass black hole pitch

what is the ratio (by what factor is the BH pitch higher than A?)

I should take over here.
The ratio of 4.78e-40 divided by 1.49e-40
is 3.2

so the pitch of the black hole is a factor 3.2 higher than conventional A (the A above middle C on the piano)

I have to say what note it is.

Well it is a factor 1.6 higher than the A above the A above middle C.

I am trying to figure out how many musical halfsteps corresponds to the factor 1.6, be back in a moment

 

[marcus]

I got that it was 8 halfsteps above A (above A above middle C)

actually 8.137 halfsteps
but who can hear 0.137 of a halfstep in music, not me
so I just say 8 halfsteps

A BC D EF

It must be an F
because F is 8 halfsteps above A

So you go to the official A440 on the piano, the first one above middle C, and then you go one octave up to the next A
and then you go to F

and that is the note that a black hole with solar mass
would vibrate at

 

[marcus]

now we have something reliable (not just a rough estimate)
the musical pitch of a solar mass black hole really is that F
we could write it on a staff, on music paper
or play it on the piano

I just went downstairs and played it on the piano
it is not the highest F on a conventional piano keyboard but
it is only one octave below the highest F

I don't think a soprano could sing it
sounds more like a bird than a human
cant imagine how a BH 3 kilometer in diameter could vibrate with that high a frequency,
incredibly rigid!

hope the weirdness of calculating such a thing did not freak you out.

if you have any questions a propos this please feel welcome to ask

 

[8LPF16]

Marcus,

I have a much better understanding now. So many specialists, so little communication.


How important is the use of musical note in this? Is it just a neat idea for a model?

When you say 2765 cycles/sec for 880 radians, that is its' vibratory rate per second. In our music scale, that would be indistinguishable from 2792 freq, or F three octaves up from mid C, yet your saying A. That's where I'm still wondering...

Music moves through 26 half-step intervals of 1.05946,
Mass (apparently) moves through 57.3 intervals of 6.28318 ?
to reach TWO full cycles.

(26 x 1.05946 = 27.54596 x 13 = 358.09748)
(57.3 x 6.28318 = 360.026214 / 13 = 27.6943...)
They are close, but I think after such large numbers in small increments, they wander "off tune".

I see that an interval of 1.065 would bring them closer (27.6926),
but would Mozart approve? What "equation" would give this interval, as 12th sqrt 2 gives 1.05946?

On the theoretical side, I have obtained these patterns from trying to envision the form of the photon. In this theory, a potential photon that is not "energised", is equal to a "gravitino". Maybe the proposed near speed of light speed of gravity could play into this (we are within 96-99%)

At any rate, I see a problem harmonizing a system that uses 13 as its' divisor, with a system that uses 57.3 [?]


LPF

 

[8LPF16]

Marcus,

"Holy unlyrical lyrics Batman"...

Now I see that your on an F too!

And, upon further review, I see that 57.3/13=440 !

Maybe we weren't so far off after all.

Thus concludes my first lesson in..(you never did tell me what this is).

LPF

 

[8LPF16]

Marcus,


I also see that your way (27.6943...)came closer to my predicted interval of 27.6923... than Mozart's of 27.54596.



And now, in perfect resonant form, the full Moon is rising out of my left window. Its' bright glow reflecting off snow covered ground casts the trees as the darkest objects in my perception; green does not exist in this world.


Thanks for the great thread!

LPF

 

[marcus]

thank you too, for a very congenial thread (and accompanying Montana images)
shall we begin a new thread, it could be about
BH temperatures and/or natural units
or do you have an idea for one

 

[8LPF16]

Marcus,

I just wanted to get on the same page before we went further. I think there were more points to consider.

Reply to your "commentary:
what this is really about is appreciating the universe's intrinsic frequency which on the scale we are using is unity-----one.

It is a very high frequency.

Try to grasp it."

This is wonderful news for me, to see Science find these patterns in their study of the Universe. We are of the Universe, and everything in our world follows this form. This is the value that all systems make their beginning from, and from that point, all is One, it is the ultimate commonality. You must, of course, go beyond any simple mathematical expression to understand this fully. When you realize that One is your number, and that everything shares this trait. You must first know One before you can know others. After this point, you can go "inside" of One, to see the division of One. The Fibonacci series reveals this truth in Nature. The exact values of this series must be "rounded off" in our system. .61803 becomes the original One, and 1.2360 is the offspring double value that is still a One. Following the same pattern, (adding previous values to obtain next value) 1.8540 becomes Two, 3.0901 is Three, 4.9442 = Five, 8.034 = Eight, and 12.9785 is Thirteen.

So Natures' favorite series is 1,1,2,3,5,8,13. It is The "Mother of all Scales" in creation: All things have a relationship of their One to the One of the thing that created them. Outside of that, Two begins the Dualistic nature of our Universe, through oscillation, polarities have simultaneous existence (two notes = interval chord). Three is the beginning of dimensionality, and the "strong" relationship of the Triad (chords, color force, atomic). Family = M / F / child that is neither yet, and, of course the religious aspects of Trinities. Five Forces (as you mentioned), Eight harmonic steps through Thirteen potentials. That is as hard as it needs to be; the similarity, diversity, the urge to continue, or reproduce, and the subsequent relations of relative objects. That describes everything you can encounter from 1 to infinity (no zero). To quote a song from a few years ago

"Oh, I wish I were a Trinity,
So that if I lost a part of me,
I'd still have Two of me to carry on."

To reproduce is to make a Double of original value. This is 1 full cycle, the "octave" in music. The photon, and our perceptive range of color follow this same pattern. Please check this out -
https://www.physicsforums.com/showthread.php?s=&threadid=13481

If the mass of a Black Hole can be describe this way, I will not have to look over my shoulder.


LPF

 

[8LPF16]

After seeing (part) of this chart, you can see that it is easy for me to look in a column and find resonant values.

At the very small values, it doesn't take much to be "out of tune".

For values at the e-40 row, G# = 1.488739, and A = 1.578423, which is why I was questioning your "tuning" of A @ 1.49e-40. Obviously millions of times beyond our perception.


LPF

 

[marcus]

hello 8LPF16,

I looked at your table of frequencies and also saw your post
in the "kepler length" thread, where you mention red-orange light
of I think 660 nanometers.

I've been thinking of possible ways we could discuss color
or wavelengths and frequencies of light. Havent forgotten. just
didnt get any good ideas yet.

there was a odd coincidence that caught my attention:

in that story about the Stove of black holes at one point I mentioned that E28 is a sixth of a micron

the natural unit of length (I think of it as the universe's length unit, the square unit being the area quantum and the cubic unit the volume quantum more or less)
this natural unit of length, Planck length, is very very very tiny
and so 10²⁸ units only makes a sixth of a micron
a sixth is around 0.166 (being imprecise)

0.166 micron is 166 nanometers

so we could discuss wavelengths of visible colors, if we wanted to, in terms of the natural length unit
we would just use the E28 scale (work in "sixths of a micron" so to speak) or the E27 scale ("sixtieths of a micron")

I mean, instead of having everything in nanometers

you mentione a "red-orange" light and I am wondering what that
wavelength would translate to in the natural unit.

 

[8LPF16]

Marcus,

In the constants chart (NIST), I see

"planck length" = K 1.416 79e32
"natural length" = m 386.159 2678e-15

I'm not sure which one you would like?


This reminds me of the "barn cross section" of 10e-28 m^2 - is this still in use?


LPF

 

[marcus]

Originally posted by 8LPF16
Marcus,

In the constants chart (NIST), I see

"planck length" = 1.61624e-35 meter

...


LPF

hi LPF,

I think you made a typo copying from the NIST site

I corrected it, see if what you find at NIST for Planck length
is this

1.61624 x 10^-35 meters

 

[marcus]

What this means to me
(I need something familiar and physical to relate to
besides the numbers)
is that E33 times the Planck length is
the width of my little finger at the joint
which happens to be right about 1.616 centimeters

just kidding, I can't measure it that accurately, but
somewhere around 1.5 to 1.7 centimeters, so that's my
concrete idea of 10³³ times the Planck length.


when Planck introduced this length and the other units, the temperature, the mass, etc
back in 1899
he called them "natuerliche Einheiten"
natural unities
or natural units

since then a lot of other quantities have been proposed as
"natural" mostly related to particular objects like an electron
or a proton or a hydrogen atom-----but Planck's do not depend on
any one chosen object, they are universal. So when I say natural units I am referring to Planck's system from back in 1899
(which is what NIST lists)

strange that a unit of length would be so tiny that you have to scale it up by 10^33 before it is big enough to measure everyday stuff with
but this is the unit that seems built into nature
good to know about it
lets discuss it some more!

 

[marcus]

you remember the universal unit of frequency
the Planck frequency
very high
we compared ordinary pitches to it and
found that official A was about 1.5e-40
middle D was about e-40

well, the Planck length is the wavelength
corresponding to that frequency

that's maybe a good way to think of it

the frequency is very high so it has a very short wavelength


physical quantities are related to each other by physical laws
so if you pick a frequency you get the other quantities for free
you get a length, and an energy, and a mass (from the energy by
E = mc^2) and so on.

or if you choose a unit of energy, you get the other things

or if you choose a length unit, you get the other things

it is a coherence of physical quantitites

we just happened to approach it from the side of frequency and musical pitch

 

[8LPF16]

Marcus,

Thanks for cleaning up my paste spillage. I see I need to update my handbook (h=6.626e-34) this is now 6.616e-35? or these are not the same? (h and Planck length)

I wondered about the term "compton". You were using it in values with mass, and I had this krypton 86 orange-red line of 6057.802 angstrom (605nm) that I understood to be a set point of reference for "color" of wavelength. Points of reference in the context of Planck values - reducing concepts to their most basic and fundamental values. Similar or separate? (compton and Planck)

I am very interested in producing a loom (model) with you to better understand the weave pattern in the fabric of our Universe.

Studying the strings/fibers is fine, but at some point, you need to test your knowledge and try to make a universal rug, in the same manner as Nature.

LPF

 

[marcus]

Originally posted by 8LPF16


I wondered about the term "compton".
...

I hope you agree that it is congenial to go at things bit by bit and not try to solve all the problems of the world in one resounding statement. So about "compton"

It refers to Arthur Holly Compton and something he noticed in 1923.
An american. back in 1923 most of the important people in physics were european so that is already a little unusual. I guess they had haircuts like in the old PBS series "Forsythe Saga" or the overdone recent movie "Titanic". Holly is a pretty good middle name too.

the compton length associated with a particle

it depends only on the mass of the particle, so the length is different for particles with different mass.

in Planck units the formula is simply 1/M

more massive particles have shorter comptons

less massive particles have longer comptons
(has something to do with their being "more spread out" harder to pin down to one particular location)

First let us be thankful for the surprise that a particle, which is a point-like thing, could have a length associated with it at all!

Then let us wonder that a man in St.Louis Missouri or Chicago or somewhere like that, with nothing but an Xray tube that he could squirt Xrays at a piece of metal with, could find such a strange thing as a length associated with a particle.

It is sort of like a wavelength, and people call it the particle's "Compton wavelength", but where's the wave? It isn't exactly the wavelength of any wave.

I haven't said what the compton of a particle is, have I
why not just spade up the ground a little and talk about that later?
it is a good measure of how difficult it is to localize something

(small-mass things are difficult to localize, maybe this has something to do with an as-yet-not-understood character of space, so far it is just embodied in ad hoc laws of quantum mechanics which
are ultimately, well, ad hoc)

 

[8LPF16]

Marcus,

Thanks for the answers, and yes, let the details rest in the soil for now.


Back to fundamental units.

You said "the frequency is very high so it has a very short wavelength", referring to 1.5e-40 . This seems to be a very tiny frequency, unless it is 1.5e+40? Am I taking this wrong?


LPF

 

[marcus]

Originally posted by 8LPF16
Marcus,

Thanks for the answers, and yes, let the details rest in the soil for now.


Back to fundamental units.

You said "the frequency is very high so it has a very short wavelength",...

LPF

I mean the frequency One
it is an extremely high frequency
it is the unit frequency in Planck, or natural, units
it is 1 radian per Planck unit of time.

not since the big bang has light been seen with such a high
frequency as this
but cosmologists say at big bang it was very hot
so that light could have higher frequency than Xrays even
and shorter wavelength than Xrays or anything we now know

the light in the core of the sun is Xray light because
the temp is million of conventional degrees

but even that Xray light in the core of the sun is
freqency e-25
compared with frequency One

that is why I say One is a high frequency.
the frequency of light in sun core is
$$\frac{1}{10000000000000000000000000}$$
of the universe frequency.

Universe frequency has very short wavelength, called "planck length".
the higher the freq, the shorter the wvlngth. Goes by reciprocals.
So wavelength of suncore Xrays is a big number e25 of Planck lengths.

 

[marcus]

Today suggested thought topic could be
that the number 1 can refer to a very high speed
the speed of light

just because 1 is not a big number does not mean that in some system of units it cannot name the highest speed

when 1 is the name of the highest speed then the speed of sound
in air is around
$$\frac{1}{1000000}$$

and the speed you drive on the highway is around

$$\frac{1}{10000000}$$

(I realize this is elementary to you but doesn't hurt to remember it occasionally)

And by same token in some system of units (again I mean Planck, or natural as he called them) the number 1 can refer to a very high temp, or a very high freq.

Just because 1 is a small number we all know does not mean it cannot be the highest imaginable temperature or frequency

and then room temperature, that you probably are in right now, is
2e-30

$$\frac{2}{1000000000000000000000000000000}$$

and the temperature at the core of the sun, where the energy is made that you digested when you ate lunch, is e-25

$$\frac{1}{10000000000000000000000000}$$

 

[8LPF16]

Marcus,

"I mean the frequency One
it is an extremely high frequency
it is the unit frequency in Planck, or natural, units
it is 1 radian per Planck unit of time."

I'm with you now. One cycle being completed in the least amount of time possible in angular increments. (nothing faster?)

Would "planck wavelength" then be One cycle in the least amount of space? (width of vibration, so - nothing smaller?)


I'm not sure of the correct equation, BUT...

IF frequency = 299,792,458/wavelength
AND wavelength = 299,792,458/frequency

can this be simplified with One?

LPF

 

[marcus]

Would "planck wavelength" then be One RADIAN in the least amount of space? (width of vibration, so - nothing smaller?)


I'm not sure of the correct equation, BUT...

IF frequency = 299,792,458/wavelength
AND wavelength = 299,792,458/frequency

can this be simplified with one?

-------------

Correct
In Planck units it is a fact that

frequency = 1/wavelength

wavelength = 1/frequency

---------------------------------

however to communicate easily in Planck units
(since they are based on hbar (not h) and angular formats
for freq. and wavelength

to communicate easily, one should get used to
angular format

so the wvlngth is the distance thru which the wave accomplishes
one radian of phase
-------------------------

now a "cycle" which is a concept on the backshelf
equals 2 pi radians

so the wave accomplishes a full cycle in 2 pi of what we are calling
its wavelength

somepeople call it the "reduced wavelength" or the angular wavelength.
and may write it with a small greek lambda with a bar thru it
or call it "lambda-bar"

its tough that there should be this divergence in language but
one gets used to it
---------------------------

my solution is never to mean anything else but angular freq, when I say freq.
and never to mean anything else but angular (or reduced) wavelength when I say wavelength.
-----------------------

your basic idea is right and good
namely

lambdabar = 1/omega

omega = 1/lambdabar

the only possible confusion involves a wayward factor of 2 pi
which is really just a redherring, not a substantial codfish.