Talk:Frequency

440 Hz

Is it not true that the A tuning note is only 440 Hz in the United States, while in fact 442 Hz in Europe? Perhaps this should be changed. — Preceding unsigned comment added by Trhaynes (talk • contribs) 18:27, 3 December 2004 (UTC)

See Pitch (music) — Omegatron 14:36, 20 February 2006 (UTC)

Changing wavelength

I was just wondering about the comment that when a wave goes from one medium to another, the frequency remains more or less the same, only the wavelength changes -- this doesn't make sense to me. If frequency has an inverse relationship to wavelength, how can one change without the other? — Preceding unsigned comment added by 131.172.4.45 (talk) 03:50, 13 April 2005 (UTC)

It's correct. Suppose the wave propagates 340 metre per second in the first medium, and 680 m/s in the second, and suppose the frequency is 340 hertz so that the period (i.e. the time it takes for one complete oscillation) is 1/340 seconds. These values fit a sound (a rather deep tone) passing from air into a somewhat harder medium. Then, in air, this sound travels 1 metre per period, so the wavelength is 1 metre. In the harder medium, it will travel 2 metre in the same time, doubling the wavelength.

Put differently: Yes, frequency has an inverse relationship to wavelength in a given medium, but the constant of proportionality depends on the medium.--Niels Ø 09:35, Apr 15, 2005 (UTC)

Invariance of frequency

Just wondering if any one has thought about why frequency is invariant (apart from doppler effect). ie whatever you do to a signal, you can change its wavelength and or velocity but you cant change its frequency. (I'm not considering mixers here). Any musings from anyone as to why this should be so?? --Light current 06:52, 23 November 2005 (UTC)

Because it's based on time? Theory of relativity and all that?

I'm not sure if it's worth pointing out, but the frequency of a pre-recorded signal can certainly be changed by playing it back at a different speed. Practically, if you sample something with an incorrect sampling frequency (you think it's 48 kHz but the oscillator's actually running at 48.01 kHz), then reproduce it correctly, the frequencies will be shifted.

Plus there are things like pitch shifters to simulate a change in frequency, though that's even less relevant. — Omegatron 21:32, 7 December 2005 (UTC)

Quite correct about pre recorded signals, but Im thinking more of a 'pitch shifting' method but broad band and not using mixers (multipliers). I guess it just can't be done? --Light current 22:07, 12 December 2005 (UTC)

It could probably be done with wormholes. :-) — Omegatron 15:02, 18 February 2006 (UTC)

I've heard that strong gravitation could change the frequency, so wormholes, why not :) — Preceding unsigned comment added by 130.234.198.85 (talk) 00:05, 7 June 2006 (UTC)

Oh you're right! You could change frequency just by flying around at a different altitude from your observer. Gravity Probe A was exactly that. — Omegatron 02:22, 7 June 2006 (UTC)

This is a Doppler effect. GoldenBoar 16:13, 7 June 2006 (UTC)

I don't think so. Time flows at a different speed depending on your distance from the Earth or another body. If you took a huge loudspeaker and put it in a hot air balloon, time would pass at different rates for you and the speaker, so the frequency would be shifted, since frequency is really just another word for time. — Omegatron 23:21, 7 June 2006 (UTC)

What about the Invariance of Speed, with regard to a constant medium? The above discussion and corresponding paragraph in the article both make some broad assumptions about the source of the Waves. It is also true that if the medium remains the same, speed is invariant with regard to wavelength and frequency... That is, if you have a slinky... and start sending pulses through it at a fixed speed, changing the frequency with which you initiate the pulses will only affect the wavelength, and vice-versa (i.e., frequency is NOT invariant). Representing this fact as well would probably make the article more sensible-seeming to those who really don't know anything about waves. I mean, strictly speaking, since the article is a general description of the quantity Frequency, with respect to other common quantities or terms used to describe the nature or behaviour of waves and signals - e.g., period, phase, amplitude, wavelength, cycle, etc. - this rather random statement about the Invariance of Frequency is not true, at least not without some context. - joe — Preceding unsigned comment added by 131.112.6.220 (talk) 10:26, 15 July 2006 (UTC)

I removed from the bottom of the section Frequency of waves:

Apart from being modified by the Doppler effect or any other nonlinear process, frequency is an invariant quantity in the universe. 
That is, it cannot be changed by any linearly physical process unlike velocity of propagation or wavelength.

My motivation is:

1. The Doppler effect is a linear process and changes frequency.
2. The statement is contradictory since it states frequency is invariant but it can be changed by the Doppler effect.
3. The statement depends on the definition of frequency. If using, for instance the Fourier transform, frequency is the new independent variable and will be invariable since it is independent. I do not know any other definitions of frequency, e.g. the time derivative of the phase, which leave it in general as an invariant (apart from trivial cases as periodic oscillations).

Kraaiennest (talk) 17:07, 22 February 2008 (UTC)

You guys probably settled this a long time ago, but Doppler shift is not linear operation the EM field. It is caused by something in motion, and that something in motion means the media constants are functions or time. Suppose a steam engine was over there and now it is over here. When it was over there, the media constants over here were pretty close to vacuum. When the train is here, the media constants differ greatly from vacuum. The moving train is in effect a time dependent distribution of the media parameters. E&M propagation is not linear if the media is time dependent. Which, of course we know because it generates frequencies at its output that were not in the input. And if you are more into math, sine waves are Eigen functions of linear time invariant differential equations. Constant314 (talk) 21:08, 29 October 2010 (UTC)

Measurement

We have a rather strange paragraph that tells us how to measure frequency by dividing one number by another which is of course true. But do we have anything about various classes of frequency meter - i.e. how we actually measure frequency? Pcb21 Pete — Preceding undated comment added 10:54, 17 April 2006 (UTC)

Yes, that would be a good addition, aince there is no separate article for that topic. --Chetvorno^TALK 19:52, 8 August 2008 (UTC)

radians per second

In my opinion, this is not a unit of frequency, but of angular frequency. --84.159.248.246 17:04, 20 November 2006 (UTC)

Human heartbeat

I removed the non sequitur "Notes" heading and its entry about the human heartbeat being close to one Hertz. Actually, the human heartbeat varies quite a bit--it can get down to 0.8 Hertz in mellow marathoners and up to 2 Hz in times of high stress activity. Average heart rate is about 72 bpm, or 1.2 Hz. No studies support the statement that the heartbeat is exactly 60 beats per minute which means there's no benefit to the reader by announcing that the heartbeat is approximately 1 Hz. It doesn't shed any light on the concept of frequency. Binksternet (talk) 08:36, 25 January 2008 (UTC)

Period estimators (for ocean surface waves, copied from Talk:Wave period

Mean zero up-crossing period, TZ or Tm0,2

When recordings were first taken this was onto charts and simple counts could be made. First the charts were zero-meaned (the average and trend calculated and drawn through the plot to provide a new axis for measuring) and then the number of times the wave record crossed the mean going up (or sometimes down) was counted and this gave the number of waves and, as a time measure, the zero-crossing period. The parameter is estimated by taking the mean of these periods for a given wave record. For wave records on paper the mean level is found by eye and Tvisual is estimated from the record length and the number of zero up-crossings counted on the record. This method can also be applied to digitised data using a computer but if the wave records are available in machine readable form it is preferable to estimate from the moments of the spectrum using,

Tz=$sqrt(m0/m2)$

where the mi values are spectral moments. The alternative symbol of Tm0,2 is derived from the moment equation. It can be seen that TZ is very dependent on the higher frequency end of the spectrum and although TZ is the most commonly used period estimator it is not very stable.

Significant wave period, Ts

The significant wave period is the mean of the zero up-crossing periods associated with the highest one third of the waves. It is sometimes denoted by Ts. Note that this parameter cannot be obtained directly from the wave spectrum. It is not very useful, but sometimes is used!

Spectral peak period, Tp

The spectral peak period is the inverse of the frequency at which the value of the frequency spectrum is a maximum. It cannot be defined satisfactorily in multi-peaked spectra. fp is very important in characterising spectra.

Period associated with the most likely highest wave, Tmax

The most likely height of the highest wave in a record of duration 3 hours is Hmax and Tmax is its period. It is often obtained indirectly from Tz or Tp using empirical relationships, or from Hmax and steepness assumptions – usually to obtain a range of possible associated periods. These methods should be applied only in the water depth for which the empirical relationships have been found, usually deep water (i.e. depth >1/2 wavelength). It should be possible to use the steepness method in shallow water provided that refraction is minimal and that allowance can be made for shoaling effects. It cannot, however, be derived directly from the wave spectrum.

Energy period, Te

This period is important for power estimation and is used in wave power design as a preferred comparator. The most appropriate way to consider energy period is as the period of the regular wave that has the same significant height and the same power density as the sea-state under consideration. It is defined as,

Te=$(m-1/m0)$

Because of the relationship with power it is worth giving the expression for time averaged power associated with a spectrum,

power = rho g^2 m0 Te / 4Pi

Hence we can find an expression for Te as follows,

Te=(64 Pi Power)/ rho g^2 Hs^2

Average wave period, Tav

This is the inverse of the average frequency calculated from the mean of all component sine waves weighted by the spectral energy. It cannot be measured in the time domain unless the waves are simple sine curves.

Average crest period, Tc

Defined as, Tc=$sqrt{(m2/m4)}$

This is equivalent to dividing the length of the wave record by the number of crests where a crest is any point either side of which the surface elevation decreases. Crests are not necessarily associated with zero up-crossings. Clearly this is very much influenced by the ‘tail’ of the spectrum through the fourth moment.

(copied from Talk:Wave period by Kraaiennest (talk) 21:46, 10 February 2008 (UTC)).

Wireless communications

I have removed the following from the "Definitions and units" section:

Frequency is important in wireless communications, where the frequency of a signal is mathematically related to the wavelength. If f is the frequency of an electromagnetic field in free space as measured in megahertz, and w is the wavelength as measured in meters, then w = 300/f and conversely f = 300/w

(1) The text, if it belongs in the article at all, is in the wrong section. The text does not belong here. There is a long list of things for which the concept of frequency is important, we aren't going to talk about all of them in the "definitions and units" section. (2) The text is true but not true enough: (2a) With waves speed is always "mathematically related" (i.e. equal to the product) to frequency and wavelength, that fact is not specific to "wireless communications". (2b) The 300 used is the speed of light in a vacuum, although we neglect to mention that point, but this isn't the page for quick rule-of-thumb formulae for radio technicians. (2c) Elementary maths gives us one formula from the other so, once again, not useful here. (3) Everything is already covered in the "physics of light" example section.

Paul Beardsell (talk) 19:22, 15 March 2009 (UTC)

Put 'Physics of sound' section on a diet

I think most of the 'Physics of sound' section should be removed. Description of longitudinal vs. transverse waves, polarization, etc. are not necessary for the explanation of frequency of sound waves, and simply repeat coverage in other articles. This is where 'Wikipedia bloat' comes from. All that should appear is a simple exposition of sound wave frequency, mention of how it's measured, and maybe something on the 'spectrum' of sound frequencies analogous to the spectrum of electromagnetic waves. --Chetvorno^TALK 22:58, 17 March 2009 (UTC)

I couldn't disagree more. There are far too many articles on audio equipment and acoustics and music that link to this page expecting it to explain what frequency has to do with sound. I recently added information about pitch, because it wasn't there and I needed it.--Atlantictire (talk) 03:04, 1 May 2011 (UTC)

Done. But see new section below. Dicklyon (talk) 17:55, 18 January 2014 (UTC)

Vandalism

The last citation link links to xkcd for absolutely no reason. —Preceding unsigned comment added by 71.228.164.178 (talk) 02:25, 9 June 2009 (UTC)

XKCD are currently running a campaign to vandalise the wikipedia of every subject the comic touches upon. —Preceding unsigned comment added by 217.23.232.41 (talk) 15:47, 10 June 2009 (UTC)

No. Firstly, assume good faith. Secondly, xkcd is a comic (singular) and not a corporation, team or trained knowledge-fighting force all bent on destroying wikipedia. 217.23.232.41, you have yourself proven to be attributing more troll-like behaviour, having recently launched your own "one soldier counter offensive" and posting anti-xkcd pseudo rants on all talk sections of articles pertaining to or mentioned by the webcomic. I'm not in favour of more xkcd refs on WP, I'm just wondering who really has the problem here. --PenguinCopter (talk) 10:15, 12 June 2009 (UTC)

Fourier analysis

Frequency in Fourier analysis is a different concept from 1/(period). I don't have time to write an explanation now but I think that concept, and links to appropriate articles, would be helpful here. Ccrrccrr (talk) 23:25, 19 February 2010 (UTC)

It depends!

Please add some data to the article saying what variables of waves in sound and light depend on the frequency of the wave. eg speed, impedance, refracting index, attenuation coefficient, etc. —Preceding unsigned comment added by 91.99.166.67 (talk) 10:50, 10 May 2010 (UTC)

Copyright problem removed

Prior content in this article duplicated one or more previously published sources. The material was copied from: http://www.wavesignal.com/Light/index.html (content was added in February 2009; archives confirm their prior publication. Infringing material has been rewritten or removed and must not be restored, unless it is duly released under a compatible license. (For more information, please see "using copyrighted works from others" if you are not the copyright holder of this material, or "donating copyrighted materials" if you are.) For legal reasons, we cannot accept copyrighted text or images borrowed from other web sites or published material; such additions will be deleted. Contributors may use copyrighted publications as a source of information, but not as a source of sentences or phrases. Accordingly, the material may be rewritten, but only if it does not infringe on the copyright of the original or plagiarize from that source. Please see our guideline on non-free text for how to properly implement limited quotations of copyrighted text. Wikipedia takes copyright violations very seriously, and persistent violators will be blocked from editing. While we appreciate contributions, we must require all contributors to understand and comply with these policies. Thank you. Moonriddengirl ^(talk) 21:43, 22 December 2010 (UTC)

Frequency and perception info in lead

There ought to be an overview of how frequency is relevant to your perception of, say, light and sound in the lead. I can't tell you how many audio-related pages link to this one, expecting it to explain how frequency is the property of sound that most determines pitch. Until just now it didn't. I've added a very brief explanation of frequency's relationship to pitch in the Physics of sound section.

But, I think this ought to be stated in the lead as well so that readers will know why they'd been linked to the frequency page right away.--Atlantictire (talk) 20:59, 26 April 2011 (UTC)

I think that's too much detail for the lead paragraph; most of the knowledge about pitch and color was worked out long before we had the ability to measure "cycles per second", and frequency isn't really a sole determinant of color; "white" is very important to color, but "white light" doesn't have a frequency, it has a spectral distribution over a whole range of frequencies. The color of a pair of socks is not uniquely determined by any particular "frequency" but by the complex interaction of light, the optical properties of the material, and the human vision system. We have sections just a short distance below the lead that explain in detail. I would suggest that any mention of color or pitch not imply that "freqeuncy" of light or sound is the unique determinant. We can't teach all of physics to someone standing on one foot, but we shuold at least avoid a quick 'n'dirty statement in the lead that is going to take paragraphs to unwind and correct later. Have you got a suggested wording? --Wtshymanski (talk) 16:14, 28 April 2011 (UTC)

Ah ha. Excellent points. To be perfectly honest, I am thinking of the needs of people who read articles on audio and I know nothing about optics, but it in broad overall principle it sounds vaguely similar to sound wave perception. Room acoustics and neurocognitive factors play a very important role in how pitch is perceived, but controlling for all that stuff, frequency is the property of sound waves that most determines pitch. Are there other properties of light waves (or whatever you call them!) that determine color, and are they as important as frequency? Sound pressure can affect pitch perception, but it's influence is secondary.

How is this: "Frequency is the property of sound waves that most determines pitch, and as a property light it plays an important role in determining color."--Atlantictire (talk) 17:08, 28 April 2011 (UTC)

Sure, try that in the article and let's see what consensus tells us. It's better because it doesn't implicitly equate frequency and color. --Wtshymanski (talk) 17:40, 28 April 2011 (UTC)

The trouble is, it's not right. It says "Waves, such as sound waves or light waves, are oscillations, and therefore they have a frequency (or frequency spectrum)." But there's no support for this; the Wave page says a wave is a propagating disturbance; there's no particular reason why a wave would be an oscillation, or be periodic, or have a frequency. And having a frequency spectrum is a much more complicated concept, which doesn't accord well with the topic, nor does it support the sentence that follows, which presumes the existence of a frequency. Dicklyon (talk) 15:14, 1 May 2011 (UTC)

Your suggested alternative wording is? Light waves and sound waves are propagating oscillations and I suppose then a subset of "waves". --Wtshymanski (talk) 15:40, 1 May 2011 (UTC)

I made a change in the lead already. Light waves and sound waves are propagating disturbances, and are waves, but are not necessarily "oscillations" in the sense that means periodic and having a frequency. Dicklyon (talk) 15:45, 1 May 2011 (UTC)

I tried again [1]...any better? --Steve (talk) 20:53, 1 May 2011 (UTC)

I'd prefer to have the lead stay simpler, and strictly truthful. To introduce Fourier transforms and spectra here is not a good idea; a section in the article about that would be OK. But it would be better not to say untrue things like "Any time-varying disturbance... can be alternatively described in terms of a frequency spectrum, given by the Fourier transform of the original signal." There are conditions under which the Fourier transform exists, and conditions under which it doesn't; it doesn't exist, for example, for a stationary noise signal, nor strictly for a sinusoid (you can extend it to include delta functions to allow the latter, but that doesn't help the former). And there are severe limits on the extent to which a Fourier transform has much say about a sound's pitch, too. I'd be happy to expound on these problems if you like. Dicklyon (talk) 21:40, 1 May 2011 (UTC)

OK. I'm not particularly happy with the paragraph but I can't think of any way to improve it. :-) --Steve (talk) 00:38, 2 May 2011 (UTC)

I would have thought any real sound or visual signal will necessarily have a Fourier transform;that non-transformable signals only exist in math texts. --Wtshymanski (talk) 01:58, 2 May 2011 (UTC)

If by real world you mean finite in duration and finite in amplitude, then yes, it will have a Fourier transform. But it won't be useful, in general, and in particular won't have any feature identifiable with pitch, for most sounds. Basically it's a periodogram, which is pretty badly behaved; it's sort of OK for light of a constant color, and perhaps of some use for a sound of a constant pitch, but not much good for a real sound like a song. Anyway, having a Fourier transform is still remote from having a frequency, and getting into spectrum in this article is probably outside its scope. Dicklyon (talk) 03:47, 2 May 2011 (UTC)

Let's see, there's nothing older than the Big Bang, and nothing farther than mumblety-million light years, so yes, I guess I do mean finite in time and in amplitude. I was more concerned with the condition of finite numbers of discontinuities, actually, but those other attributes help. We can't hear DC or see DC, at any rate; gotta be oscillating to be heard, and the ear is its own Fourier analzyer. I don't care to speculate on what other Wiki editors call the real world as my notions of what they consider real and notable seem to have low utility for predicting their behavior. Do we really need all that ponderous oscillation stuff in the lead? --Wtshymanski (talk) 14:06, 2 May 2011 (UTC)

The proposed alternatives have been to rely on Fourier transforms, or to rely on the assumption that all waves are oscillations that have a frequency. I don't see how either of those could be seen as an improvement. What else you got? What, by the way, is the frequency of the sound entering your ears (it's OK to truncate at your birth and your death). Dicklyon (talk) 15:08, 2 May 2011 (UTC)

Oh very good. This is exactly how we'd explain it to the first-year physics class. We don't need Fourier transforms at all (in the lead), and I'm not convinced there's no sound or light that aren't waves. But aren't you also concerned we've left out the relativistic corrections that are such an important feature of so many Wikipedia articles? We must beat the reader to death with every conceivable qualification and limitation in the lead; othjerwise there's the chance they won't be overawed with our smartness. --Wtshymanski (talk) 15:23, 2 May 2011 (UTC)

Wtshymanski, could you copy-and-paste some text, or link to an old revision of the article, that you really like? Then we can discuss whether or not it is misleading, and if so whether or not it can be fixed with rewording or links or footnotes or whatever. :-) --Steve (talk) 06:27, 3 May 2011 (UTC)

Good idea, climbing down the ladder of abstraction usually helps focus the discussion. I prefer something like [2]. We should not equate frequency of light with color perception, we should not go off on a tangent about non-oscillatory sounds (whatever that could be), and we must not drag in the whole mathematics textbook in the lead section. I don't like "helps determine", abstract concepts are not Boy Scouts helping little old ladies across the street. Freqeuncy is perhaps the major factor in determining (the perception of) pitch, but it's not absolute. --Wtshymanski (talk) 13:43, 3 May 2011 (UTC)

Well, I think I'll let you guys handle it. I'm too conflicted, as I spend a large part of my professional life in hearing research where I'm constantly trying to deconfuse people about frequency versus pitch, so this has become a hot button for me. My favorite quote: "...dehydrated cats and the application of Fourier analysis to hearing problems became more and more a handicap for research in hearing" (von Bekesy). Dicklyon (talk) 15:27, 3 May 2011 (UTC)

Dicklyon, I doubt you're conflicted in a bad way and I hope you reconsider.

The quote is:

P1 "The frequency of a sound wave helps determine its pitch, while the frequency of a light wave helps determine its color."

The main problem that I see is that if the sound wave is, say, five seconds of human speech, it doesn't really have a pitch and it doesn't really have a frequency. Another problem is that people who don't know how sound work will wonder what it means for sound to have a frequency. So then I thought, how about

P2 "The frequency of an oscillating sound wave helps determine its pitch, while the frequency of a light wave helps determine its color."

This sort of answers my first complaint above but not the second. Anyway, this isn't very good because "oscillating sound wave" probably makes people think of like tremolo or vibrato, which is totally different. Another problem is that, even if the waveform is exactly oscillatory, the oscillation frequency is not necessarily related to the pitch...for example when you play two pure tones together, the waveform oscillates at the beat frequency, but you can't hear the beat frequency at all if it's in the audible range. So then I thought

P3 "When air pressure oscillates sinusoidally, it corresponds to a sound wave called a pure tone. The frequency of the air-pressure oscillation determines whether the human ear can hear it, and if so, the frequency determinnes the pitch of the tone, with higher frequency giving a higher-register pitch. Likewise, when an electric field oscillates sinusoidally, it corresponds to an electromagnetic wave called monochromatic. The frequency of the oscillation determines whether the wave is visible light, infrared light, a radio wave, etc. In the case of visible light, the frequency determines the color, with lower frequency corresponding to red and higher to violet.

OK, now this is accurate I think...but maybe too many words and too many new concepts for readers ("what does sinusoidally mean?, etc...") Or maybe it's OK? Or maybe a better approach is to take P1 and just slap a giant footnote on it... I'll think more later. :-P --Steve (talk) 01:54, 4 May 2011 (UTC)

Oh yeah, P3 is the Wikiest one of all. And everyone knows the frequency of a sound must be determined at the Big Bang and never change until the end of time. Let's try and work in the Doppler effect and at least first-year relativity, too, while we're at it, and make it perfectly general. (To make it even Wikier, maybe add Tesla in somehow.) --Wtshymanski (talk) 02:30, 4 May 2011 (UTC)

For sound waves, the pressure can't change instantaneously - define "frequency" as "time rate of change of phase" and you can get the notion that an "instantaneous frequency" can be defined for every instant (ok, maybe not uniquely). Every sound you can hear is just a 1000 Hz carrier that started at 4:13 AM UTC, July 17th, 4350 BC, suitably modulated! --Wtshymanski (talk) 15:03, 4 May 2011 (UTC)

Wtshymanski, please stop being sarcastic. You can just say "P3 is too technical and readers will be lost". In fact I agree with that. :-) How about:

P4 "The frequency of a sound wave (an oscillation in air pressure) helps determine its pitch, while the frequency of a light wave (an oscillation in electric and magnetic fields) helps determine its color.^{[NOTE 1]}

^{[NOTE 1]:} This is a simplification, valid if the wave is sinusoidal (a pure tone for sound or a monochromatic light wave). For more complicated waveforms, the perception of pitch and color is related more specifically to the Fourier transform of the waveform over a short time interval.

I think this answers both of the problems I pointed out above. "Note 1" is a footnote and would go in a separate footnote section, like they do in this article-section [3]. --Steve (talk) 17:39, 4 May 2011 (UTC)

Not sarcasm, just another observation on how the group-think editing model usually produces unreadable prose; it's not confined to this article, it's a common Wikipedia fault. How about "The frequency of sound relates to its pitch, and the frequency of light is the most important factor in the perception of color." (as distinct from ampitude, say) or something like that. Never mind the waveforms and Fourier transforms, Aristotle and Newton had the gist of the properties of color and sound worked out well before the maths came along. --Wtshymanski (talk) 18:18, 4 May 2011 (UTC)

So you don't like the idea of having a footnote? Why not? I like how you made it sound more vague ("relates to"), that way people will continue to look for more details if they need to know more details.

Do you think it's a problem to say "the frequency of sound", when it's not obvious that sound has anything to do with oscillations? I mean, when you hear a long musical note, it sounds like a constant stream of sound, so isn't it weird to say it has a frequency? Frequency was just introduced in the previous paragraph as something related to periodic oscillations, so intuitively the concept of "frequency" seems unrelated to a constant stream of sound. Imagine you don't know how sound works, then you would read the phrase "the frequency of sound" like you or I would read the phrase "the frequency of a pencil".

On the other hand, I suppose it can be OK and sometimes necessary to have poorly-explained things in the introduction, which are explained better later in the article.

By the way, I have the same goal as you: Clear and pedagogical and easy-to-read and accurate text. I don't think many wikipedia physics articles achieve this, and I try hard to improve them bit by bit. I hope I'm successful most of the time, even if I sometimes make bad edits. Please stop bringing up the sorry state of wikipedia science articles in general, because it sounds like you're blaming me and Dicklyon personally for every bad science article. I doubt that's your intention, but still...let's please just discuss the frequency article. :-) Thanks, --Steve (talk) 01:16, 5 May 2011 (UTC)

Steve, I don't think it's possible for W to talk w/o sarcasm, based on my experience. If you go ahead and try something, he'll tell you if he doesn't like it, but he has a hard time being constructive. So go for it. I don't like footnotes, either, as they too often become a hiding place for unsourced interpretation and rambling. I think that if you have a short thing in the lead that mentions frequency of sound, as long as it doesn't strongly claim that sound has a frequency, should be OK. You can elaborate more carefully later. Dicklyon (talk) 05:04, 5 May 2011 (UTC)

If it were only two or three editors , you wouldn't necessarily get the group-think mush; it takes scores of editors to produce the Wikipedia effect at its highest level. It is useful to point out flaws in articles in general so that we can perhaps avoid the flaws in this article. Surely we can explain a basic concept like pitch and color without footnotes? If a relationship is so complex it can't be even mentioned without a forest of qualifications and explanations, maybe it doesn't belong in the lead section at all. "A little inaccuracy sometimes saves a ton of explanation." and I don't think obsessively qualifying the lead paragraph with every historical and relativistic factor helps the lucidity at all. And I've never said a non-sarcastic thing in my life, ask anyone. --Wtshymanski (talk) 13:23, 5 May 2011 (UTC)

I agree with Wtshymanski. A major problem with WP is intros that are mushy, or pedantic, technical, and loaded with qualifying phrases. "It is even more important [in the intro] that the text be accessible." (WP:MOSINTRO) I would say even considering footnotes in the introduction is an indication that it's getting too pedantic. How about something like: "Frequency is also a characteristic of waves, such as sound waves, radio waves, and light waves. It is used to describe the pitch of musical tones and the color of light." --Chetvorno^TALK 16:13, 5 May 2011 (UTC)

I like that a little better, and maybe that's as close as we can get...color perception is distressingly complicated but we don't need to get into the problems of color perception in this very peripheral article. --Wtshymanski (talk) 16:52, 5 May 2011 (UTC)

Right. The majority of readers, the ones who need the introduction, are nontechnical readers who are looking for the simplest possible explanation. The techies will skim or skip the intro and go to the more technical sections below. --Chetvorno^TALK 19:13, 5 May 2011 (UTC)

"Frequency is also a characteristic of waves" is true with a little stretching. And "It is used to describe the pitch of musical tones" is certainly true, since pitch is quantified as hertz. But "used to describe...the color of light" may be too much of a stretch, since color is not a one-dimensional thing like frequency, or like the simple conception of pitch. You often see confusions like "what is the wavelength (or frequency) of purple? of brown? etc." that we don't want to feed. Can we just leave out the bit about color? Dicklyon (talk) 00:38, 6 May 2011 (UTC)

Why are people coming to this page?

Somewhere between 1,000 and 4,500 people visit this page every day. I think it might be useful to take a look at the pages that link here to try and get a sense of what the readers' needs are, and then to expand the lead so as to better orient them. It's nice after you've clicked on a link to a page to know from the lead why you're there. As someone who's just started learning about audio engineering concepts, I have to say I couldn't tell right away what frequency had to do with anything... and then I figured it out and added information about pitch. Yes, some of us really are that dumb!:)--Atlantictire (talk) 02:58, 1 May 2011 (UTC)

f versus ν

So what is the criterion for using f instead of the Greek letter ν? As far as I know ν is a more widely used symbol for frequency. — Preceding unsigned comment added by 188.83.90.251 (talk) 16:10, 12 June 2011 (UTC)

The relative frequency of usage of f and ν varies across different disciplines. Dicklyon (talk) 17:19, 12 June 2011 (UTC)

I added a mention of ν. Fgnievinski (talk) 16:14, 21 October 2014 (UTC)

Physics of light and physics of sound

I reworked these old sections by departed User:Logger9, and renamed them to be just Light and Sound, since they're supposed to be about frequency, not about physics. It's interesting that the sound one says "Frequency is the property of sound that most determines pitch," which is true for repetitive sound waves according to the definition of frequency given, but completely misses the opportunity to address the oft-discussed disconnect between frequency and pitch in psychoacoustics. Project for another time... Dicklyon (talk) 17:58, 18 January 2014 (UTC)

Renaming

Rename to Temporal frequency and keep Frequency as a redirect here. Not asking to change the scope of this article, just to have its title reflecting the scope more accurately. Thanks. Fgnievinski (talk) 16:16, 21 October 2014 (UTC)

My feeling is that's not necessary. "Temporal frequency" is the most common meaning of "frequency" and the other common meanings can be distinguished in the introduction, and for less common there's the hatnote directing readers to the DAB page. I think it's irritating to readers to use some obscure term for the article title, and it makes it hard to link to the article. From WP:NC the title chosen should be the one "...that readers are likely to look or search for and that editors would naturally use to link to..." --Chetvorno^TALK 18:16, 21 October 2014 (UTC)

I agree with Chetvorno's assessment and recommendation. That said, I've created a redirect at Temporal frequency to the disambiguation page as its Lead clearly differentiates the term. --SCalhotrod (Talk) ☮ღ☺ 18:55, 17 November 2014 (UTC)

Frequency is a concept based on occurrences over time, so the adjective temporal (of or related to time) is not needed, redundant. Binksternet (talk) 20:59, 17 November 2014 (UTC)

@Binksternet and Chetvorno: Binksternet's misunderstanding is exactly the reason why I proposed the renaming. Frequency may have originally started as synonym of temporal frequency, but it's outgrown that definition, e.g., spatial frequency is obviously a non-temporal type of frequency. Fgnievinski (talk) 21:41, 17 November 2014 (UTC)

I agree that the word frequency came from frequent, which has long been a temporal phenomenon. The idea of something being frequent in time was borrowed by science to construct the much more recent idea that "spatial frequency" is not about time but about occurrences over area. As such "spatial frequency" is relatively unimportant; a small percentage of humanity uses the term. (It appeared first in 1878 in a study of hemophiliacs, talking about their prevalence in a population or geographic area; the term was quickly criticized for its inaccuracy.[4]) So you'll forgive me for protecting the much more common use. Binksternet (talk) 21:57, 17 November 2014 (UTC)

I'll forgive you. The temporal is the usual meaning, and no qualifier is needed. Dicklyon (talk) 02:56, 18 November 2014 (UTC)

Split wave frequency

As per wikt:frequency, the first definition of frequency is "The rate of occurrence of anything; the relationship between incidence and time period [or interval]" -- there's nothing about periodic/oscillating/cyclic in it, it's just the ratio of incidence count over time duration. Fgnievinski (talk) 06:57, 19 July 2015 (UTC)

Perhaps the article Periodic function is already what you would split off?Constant314 (talk) 13:50, 19 July 2015 (UTC)

@Constant314: If you agree with re-targeting the redirects at wave frequency and wave period, then a hatnote in frequency would mostly settle the matter; in the reciprocal second article, a clear distinction between periodic and aperiodic frequency units is sourced to the BIPM. Fgnievinski (talk) 21:24, 19 July 2015 (UTC)

Splitting off Measurement section into new Frequency measurement article

I don't see the need for doing this. The article is not particularly large, nowhere near splitting size, and the Measurement section itself is not large. --Chetvorno^TALK 04:59, 23 July 2015 (UTC)

Proposal to replace subsection

I propose to replace the subsection Frequency#Examples#Light with the following. I think the present section invites readers unfamiliar with quantum mechanics into waters too deep. (I am unsure about that page 111 in the 2nd edition. I am also unsure whether I should have left this code in a sandbox, but I feared a sandbox may be too volatile for the archive.)

---

Examples

Electromagnetic radiation

Main article: Electromagnetic radiation

Radio waves and microwaves

Radio waves and microwaves are electromagnetic waves, consisting of spatially orthogonal electric and magnetic fields oscillating together in both time and space, traveling through space. The wavelengths are in the range of many meters to a few millimeters, corresponding to frequencies that can be directly measured in the time domain by observing the electrical signals induced in an antenna detecting the waves.

Light

Main article: Light

Visible light is also electromagnetic radiation with much shorter wavelength, in the 400 to 700 nm range. In scientific observations, it is detected as a stream of massless elementary particles called photons, each with an energy conventionally in the range 2.9 to 4.6 electronvolts. (At low light intensities, these particles can be individually counted by a sufficiently sensitive photodetector.) In common with other subatomic particles, even massive examples such as cold neutrons, streams of multiple photons arrive at detectors in spatial distributions that reflect wave-like propagation, displaying interference and diffraction. Hence a wavelength associated with any particle of such type can be directly measured using an interferometer. This applies also to massive particles such as neutrons.

From the measured wavelength and speed of photons, what is conventionally called a "frequency" can be calculated in the usual way:

$\displaystyle f=c/\lambda$

where c is the speed of light (c in a vacuum, or less in other media), f is the frequency and λ is the wavelength.

Regarding the interpretation of these quantities, Feynman provided the following advice:

We cannot say whether light is particle or wave. This is not an either/or situation; light seems to be both particles and waves and thus is probably neither. 

Visible light shares that duality with, e.g., cold neutrons, the "frequency" of which is rarely mentioned.

Layzeeboi (talk) 07:36, 12 February 2017 (UTC)

In an electromagnetic wave, the electric and magnetic fields don't have "a relative phase of 90°". The vectors are orthogonal, but the electric and magnetic fields are in phase; the peaks occur simultaneously (in most circumstances; in materials with an imaginary index of refraction they can be out of phase). On your addition, my feeling is that the subject of the wave/particle nature of light is a little WP:OFFTOPIC for an article on frequency, although it probably doesn't hurt. Cheers. --Chetvorno^TALK 16:12, 12 February 2017 (UTC)

Thanks for catching the error. I feel that duality, in common with cold neutrons, is topical here as a caveat that wavelike properties constitute no guarantee that frequency is meaningful. Layzeeboi (talk) 00:16, 13 February 2017 (UTC)

I don't understand that point, nor what change you are proposing to make to the article. What does it mean for frequency to be "meaningful"? When is it not? Dicklyon (talk) 01:55, 13 February 2017 (UTC)

My proposed text consisting of two subsections to replace the "Light" subsection appears above, embedded in this talk section. By "meaningful", I mean treated as such by the cited sources. For example, cold neutrons show wave-like behaviour, but the sources cited there don't consider frequency. I think it can be helpful to reveal not only the meaning of a concept, but also its limitations. Layzeeboi (talk) 08:14, 16 February 2017 (UTC)

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Hertz

@Boppennoppy: Hi, see it implicitly means 1 event, and 1 here is full of meaning, but (number of) event has no dimension, because it is a number. So Hertz not means "one per second", but it means "one event per second", i.e., one (or 1) here, is full of meaning. Hertz does not mean 1 "kilometer" per second or one "kilogram" per second or anything else, it means one "event" per second. Hooman Mallahzadeh (talk) 16:14, 30 December 2021 (UTC)

One "what" per second?

Many people, when they read "one per second", have a natural tendency to ask (themselves), "one what per second?" And the associated tendency is to insert some general term for a periodic event such as "cycle". But consider a digital readout on a clock showing the number of seconds passing since some starting time. The number on the display is increasing at a rate of ONE per second—which makes perfectly good sense. Since (temporal) frequency is the quotient of the number of periodic events and the corresponding elapsed time, the dimension is number/time, 1/T, where "1" is the symbol for the dimension number, to be shown in the same special font (e.g. Helvetica) as that used for other dimension symbols. [It is not the numeral 1.] The SI (implicit) "unit" for (the quantity) number is one, 1. For time, it is second, s. So the SI coherent unit for frequency is 1/s or "one per second", also written as s^–1. This refers to a periodic event, so one per second gets a special name: hertz, symbol Hz. One hertz is one per second: Hz = 1/s. Some authors have gone further and equated "cycle" to "revolution" (of some imaginary rotating body). Thus hertz becomes "cycles per second", which then becomes "revolutions per second", which then becomes "2π radians per second"—a unit for angular velocity. Since, in the SI, the hertz is one per second and rad/s is also one per second, the same authors call this the "2π problem". To "resolve" this dilemma, they have proposed officially redefining the hertz as 2π rad/s (!).

Any quantity that is of the nature of a time-varying number (for example, a varying strain in a tensile test, or a torque-ratio in a continuously varying transmission, or the phase of a time-varying sinusoid), has a time derivative (strain-rate, torque-ratio-rate, phase-rate) with the dimension of number/time. The appropriate coherent unit for this time rate of change is one per second, 1/s, usually spoken as "per second". [Of course, other time units can be used: per hour, per year, . . . .] There are two special cases, the hertz, Hz, and the becquerel, Bq.

By the way, a similar "problem" occurs with quantities like number density: number per volume. Some people will ask (themselves) "number of what per volume?" And will have an urge to insert some "downstream-from-the-SI" symbol such as mcl (molecule), pcl (particle), or some other descriptive symbol—analogous to inserting cyl (cycle) in the case of frequency. If we are dealing with number density, the correct coherent unit is 1/m³, "one per cubic metre", or m^–3 (per cubic metre). On the other hand, if we are dealing with amount density, the appropriate unit is "entity per cubic metre", ent/m³ or ent m^–3, where "ent" stands for one entity, the smallest amount of any substance—which should be recognised as the appropriate atomic-scale unit for amount, paralleling the dalton for mass. The unit ent m^–3, can be changed to mol m^–3, since one mole is exactly 6.02214076 x 10²³ ent. The Avogadro constant (not number) is exactly 1/ent, one per entity. The Avogadro number is (very very nearly) equal to the quotient g/Da, gram per dalton (to within an order of 10^–10). A mole is (very very nearly) an aggregate of g/Da entities: mol ≈ (g/Da) ent. So dalton per entity, Da/ent, the appropriate atomic-scale unit for molar mass, is (for all practical purposes) equal to g/mol = kg/kmol. Boppennoppy (talk) 14:56, 17 November 2024 (UTC)

Is there something about the article that you want to change? Constant314 (talk) 16:04, 17 November 2024 (UTC)

Good question. On my first reading, it seemed like a waste of time. So I tried again, which just reinforced that conclusion. I don't know if there is an actual frustration, or a constructive criticism, or testing the waters for a new article, or checking for agreement/disagreement, or something else. After reading the subject line, I was expecting a discomfort (which I would agree) with against dimensionless quantities in the SI coherent units convention. E.g. there is no distinction between cycles/sec and samples/sec... they are both just hertz. Maybe that is handy for abstract theorems and proofs, but in my world, that lack of detail makes it hard or at least error-prone to interpret those results back to the physical world and the reassurances of dimensional analysis.

--Bob K (talk) 20:39, 18 November 2024 (UTC)

Thank you Bob K and Constant314 for your careful reading of my note. The main point I was trying to make is that the coherent SI unit for frequency is one per second—not one "cycle" per second (or one "sample" per second)—sometimes written as 1/s or s^–1 (the latter called a reciprocal second)—and, since frequency refers to periodic events, one per second is given the special name hertz and symbol Hz. A "cycle" (or "sample") is not a unit. This is the main reason why the International Electrotechnical Commission introduced hertz (in the mid 1930s)—to get away from the colloquial term "cycles per second". And why the SI adopted it about a couple of decades later. Unfortunately, the older term still persists and is to be found in almost all dictionaries and online tutorials as the "definition" of hertz. It does not appear in the current (9th edition of the) BIPM Brochure. [There was quite a fuss about removing it from language in previous editions.] Fortunately, hertz is not called "cycle per second" in this Wikipedia article on frequency. My note is more of a warning to keep it that way.

There is, however, a problem associated with the term "angular frequency" for ω in the expression sin(ωt). This is not a frequency; nor does it have anything to do with angles. It is the time rate of change of the dimensionless phase of the sinusoid, ωt , with dimension 1/T and unit 1/s (or s^–1) but not Hz, and certainly not "rad/s". Its appropriate name is phase rate. Stating its unit as "radian per second" confuses it with the angular velocity of some (non-existent) rotating body. However, this is an ongoing problem with the SI's treatment of angle (and solid angle), which seems unlikely to be remedied in the near future. Boppennoppy (talk) 22:59, 18 November 2024 (UTC)

I share your frustration, but all we do here is paraphrase reliable sources. You may want to read this: WP:RGW. Constant314 (talk) 01:45, 19 November 2024 (UTC)

Thank you for clarifying your intention, as a warning. I've read a few things to try to understand why it's so important to you:

• International_System_of_Units
• Dimensionless quantity
• Dimensional analysis
• Quantity calculus
• Conversion of units
• https://pmc.ncbi.nlm.nih.gov/articles/PMC7727271/
• https://pubmed.ncbi.nlm.nih.gov/38868451/

But it hasn't helped. For one thing, all those documents seem to avoid DSP, multi-rate DSP, and Normalized frequency (which is commonly used in DSP). Cycles/sec and samples/sec are completely different concepts, but I've had people insist they are both just Hz. And what about their ratio, cycles/sample? People have told me that cycles and samples are both dimensionless. So the unit is simply "one". To quote your own post, "one what?" Sorry if I'm being obtuse. But SI seems to be very controversial, so I am not alone. Can you offer better arguments or examples to help us understand?
--Bob K (talk) 20:47, 19 November 2024 (UTC)

Again, thank you for continuing this important discussion. The subject is frequency, but similar questions arise in a number of related fields. Dictionaries report on definitions according to common usage. Presumably, encyclopaedias go further and sometimes discuss controversies surrounding the definitions. One of the most controversial subjects concerns so-called dimensionless quantities, sometimes called "quantities of dimension one" or "quantities of dimension number". [The latter—naming the dimension "number" rather than "one"—is due to Michael Krystek, who proposed the symbol Z for for this dimension (German: Zahl). Whereas, in fact, the symbol 1 (not to be confused with the numeral 1) is probably a better choice: the identity element for dimensional analysis. The dimension symbol 1 is pronounced "one" but refers to the dimension "number", just as the dimension symbol T is pronounced "tee" but refers to the dimension "time", for example.]

Of course, many quantities have the dimension 1, occurring in two categories: continuous and discrete. Examples of the former include any nondimensionalized continuous physical variables, ratios of two (possibly varying) continuous variables with the same dimension (such as strain, for example: L/L = 1), arguments of transcendental functions. Discrete quantities of dimension number include anything that can (in principle) be counted (including continuous variables that have been digitised). An interesting quantity that is (in fact) discrete is the number of entities of a substance in a chemical reaction (that is changing in time). This cannot (usually) be counted directly and is such a large number that it makes sense to treat it as a continuous differentiable variable. This is, after all, the basic assumption of continuum mechanics. [Of course, the same is true of the mass of the substance because of the discrete nature of matter—but it is (usually) automatically treated as continuous without further thought.]

The unit for any quantity of dimension 1 is (the number) 1. If we are considering the number density of the above substance, this would be the quotient of the number of entities (dimension 1) and the volume of the container (dimension L³): dim[number density] = 1/L³ = L^–3. [This is a good example of the use of 1 as the symbol for the dimension number.] The appropriate unit is 1/m³ = m^–3. [Not the similarity with the above dimensions relationship.] The most appropriate name for this unit is "per cubic metre". For example, if we have 2.468 × 10²⁵ entities in a container of volume 2 m³, the number density is 1.234 × 10²⁵ m^–3, read as 1.234 × 10²⁵ per cubic metre. It is NOT 1.234 × 10²⁵ "entities" per cubic metre (or 1.234 × 10²⁵ ent/m³)—that would be an amount density: the amount of the substance in the container is 2.468 × 10²⁵ ent, where ent is the appropriate atomic-scale unit for amount (the smallest amount of any substance). The number of entities in the substance is 2.468 × 10²⁵. [One mole is (exactly) 6.02214076 × 10²³ ent.]

Similarly, frequency is the quotient of the number of periodic events occurring in a given time interval and that time interval. Its dimension is (number)/(time) = 1/T = T^–1. Its unit is 1/s = s^–1, best read as "per second". So, if I clap my hands 20 times in 5 seconds, the clap frequency is 20/(5 s) = 20/5 s^–1 = 4 s^–1, four per second, NOT "four claps per second"—a "clap" is not a unit, it is a name of the periodic event. For the same reason, this is not "four cycles per second"—a cycle is not a unit, it is a generic name of a periodic event. And, finally, "per second" is replaced by "hertz". So we write the clap frequency as 4 Hz ("four hertz"). [And, by the way, it is certainly not four revolutions per second (referring to some imaginary rotating body), as some authors would claim (by having the SI redefine the hertz as 2π rad/s—a unit of angular velocity).]

There are an unlimited number of quantities that have the dimension 1/T and unit 1/s: the time rate of change of any quantity of dimension 1 that is changing with time. The unit for the time rate of change of periodic events gets the special name and symbol hertz, Hz. The unit for the time rate of occurrences (on average) of aperiodic "radioactive decay" events gets the special name and symbol becquerel, Bq. All the rest (continuous or discrete) get stuck with 1/s = s^–1(per second). All of these can use an appropriate SI prefix.

As I mentioned in my initial note, when we read "four per second", the natural tendency is to ask (ourselves) "four WHAT per second"? The correct answer is: the number 4 per second. For frequency, this is the number of (periodic) events occurring per second—not a "description" of the events themselves per second.

All this is probably too far "in the weeds" to try to include any hint of in an encyclopaedia. But I hope it helps clarify where some of the confusion about "dimensionless quantities" arises. Boppennoppy (talk) 17:50, 20 November 2024 (UTC)

It's not that simple. It seems like semantics are getting in the way of the actual topic. Four "numbers" per second is not what happens in sound wave frequency, for instance. Sound wave frequency tracks the number of cycles of rarefaction and compression, usually referring to molecules in air. The frequency is composed of these cycles, not of an abstract number. Binksternet (talk) 19:40, 20 November 2024 (UTC)

Actually, it is that simple. It doesn't matter whether it's cycles of compression-and-rarefaction of air or widgets coming off a production line, frequency is defined as the NUMBER of (periodic) events divided by the TIME interval between those events. It has the dimension of (number)/(time) = 1/T. And is expressed in the base "number unit" (= 1) divided by a time unit, where the numerator is "the number of ones". The coherent SI unit for frequency is therefore 1/s, one per second. The corresponding period is defined as the TIME interval between events divided by the NUMBER of events occurring in that time interval. The period has the dimension of (time)/(number) = T/1 = T, and is expressed in a time unit divided by THE number unit (one), so that this quotient becomes just the time unit. [Any quantity can be multiplied or divided by 1 without changing its value.]

One of the problems causing some confusion is that there has never been an accepted symbol for the dimension number. By using 1, we can see all kinds of important relationships among dimensions. For example, if D is the symbol for a general dimension, we have: 1D = D1 = D/1 = D; 1/D = D^–1; D/D = D⁰ = 1. It may take a while to get used to. But an event of 20 claps in 5 s has a frequency of (number of claps)/(time interval) = (20)/(5 s) = 4/s (read as "four per second"), or 4 Hz. NOT "four claps per second". NOT "four cycles per second". [And DEFINITELY NOT "four revolutions per second" or "eight-pi radians per second"—as some authors would have us believe.]

The word "per" is from the Latin, meaning "for each". So, in the above example, the answer to "how many (what number of) claps for each time interval?" is:

"four for each second" = four per second = 4 Hz.

An athletic resting heart-rate is 60 beats occurring in one minute. The frequency is the number of beats divided by the time interval: (60)/(1 min) = 60/min (sixty per minute). Colloquially, this is universally called sixty "beats per minute" and written 60 BPM. But a "beat" is not a unit (of anything). The number of beats occurring in one second divided by one second would give us the heart-beat frequency expressed in hertz, in this case: (60)/(60 s) = 1/s = one per second = 1 Hz. Boppennoppy (talk) 22:29, 20 November 2024 (UTC)

We paraphrase reliable sources. I don't have a problem with samples=cycles=radians=nepers=events=1. Constant314 (talk) 23:33, 20 November 2024 (UTC)

As I have already said, I disagree with samples=cycles, and nothing written here has changed my mind. My specific question about cycles/sample remains unanswered. I haven't seen any actual examples of the supposed superiority of SI vs quantity calculus (a new term for me). So far SI reminds me of the English language, whose arbitrary rules and pronunciations were simply settled on by the necessity of settling on something... anything. Boppennoppy's "warning" seems no different to me that someone claiming French is better than English, or vice versa. I do again apologize if I'm being obtuse. Just callin' it like I see it.
--Bob K (talk) 21:55, 21 November 2024 (UTC)