I felt the need to register to chip in a bit here - the discussion I am having with @boomtopper is too big for Twitter!
I am not trying to post the 'final word' on this - the subject is just fascinating and it is a topic well worthy of debate (a traditional method for sharing and improving understanding of science!)
I love the subject of beating because it is the simplest form of dissonance, and I have done extensive academic research into dissonance theory (or as we call it, 'gride' theory) - see the link to my thesis at the end of this post.
The original question was essentially:
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If we add 2 very high frequency sines together, do they can create a beating effect that is audible to our ears?
This is entirely possible, but I don't think it is proven. Just as
when audible freqs are within critical bandwidths (1/6 of the freq), they bounce, for example when you play two piano keys that are next to each other. The beating is at a very low rate, like a tremelo. Beating is proven and common, listening for beating is helpful when tuning guitar string (for example).
Beating will occur regardless of whether we can hear the 'original' two frequencies at, say, 56 and 57KHz. The question above, and really the point of the debate, is whether we can hear only a side effect of interaction between freqs out of our hearing range.
I wanted to quote a few posts to this thread and dispel a few myths/assumptions...
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Short answer: bullshit.
Long answer: I didn't read, I just found what I expected to find scanning that site. You could repeat this with 1Ghz and 1.000001GHz and claim, we needed gear reproducing audio up to this frequency. But as a matter of fact, we neither store nor reproduce audio as sine waves. This 1kHz tone is well recorded and reproduced with standard 20-20 gear as it is (*obviosly*) within that range. The only difference is, that the two source frequencies are neither on the recording nor reproduced. Nyquist-theory as a hint.
Probably worth reading things before you dispel them, as you say "the two source frequencies are neither on the recording nor reproduced" - it never says anything about this test being recorded, and there is no evidence the person who did this test does not have the equipment with the range and ability to play back frequencies up at 56 and 57k.
Let's assume they
hypothetically do have the kit that could reproduce - some super high grade speakers with a tweeter sensitive enough to move back and forward up to 60 thousand times a second, analog gear with an operational limit up to or past 60k (I know op amp freq responses don't always go that high, but it IS possible, I don't see why certain equipment wouldn't have the capacity to do it - but this is a hypothetical question, so stick with me).
So we have a system that can produce these two 56 and 57 KHz signals. This system
would produce the frequency at 1k, because the speakers are trying to reproduce two waveforms which phase and then sum an amplitude at a speed of 1000 times per second.
So the speakers ARE producing an audible frequency of 1KHz.This is under the condition that the 56 and 57k are coming out the same speaker
What if the speakers were playing one frequency each? So the left one is playing the 56k, the right one the 57k. We wouldn't hear the sounds in isolation, but I suppose we don't know whether the 1k would be audible in this instance - the only place the beating could occur is on the basilar membrane in the cochlea. Naturally occurring beating, where the source of the beating is not a physical object trying to represent two close frequencies as described in the speaker example above, is just your basilar membrane reacting in the same way, unable to 'play' two frequencies in consonance because they are within a critical bandwidth of each other (1/6 of each others freq.)
So two sine waves on a piano, say a C and a C#, played at the same time (at the same./similar amplitude or masking can occur, where the louder note masks the other), hit two separate springs, which are both representing the C accurately on one string and the C# on the other string, have no place for beating to occur other than when it actually gets into your ear and your basilar membrane
(For a longer explanation of the basilar membrane, and how it acts/reacts and looks like, see my academic work I link to at the end of this post).
(An open question here is actually whether normal air has the capacity to represent the frequencies, because then beating is occurring before it gets to your ear - yet another area in psychoacoustics which is not fully researched. Seriously, this field is so open that
if you want to make a name for yourself in science, this is the area with enough niche to go and find something groundbreaking. It is also why so many people have these kind of debates, because actually we don't know for certain some of the points discussed in this thread, and neither side of the argument is proven or disproven other than in theory, and that we should all have an open mind, or perhaps sometimes some skepticism when talking about 'proven' facts.)
Of course,
this is assuming a system with a super high grade frequency range. I don't know for certain that such a system is easily availabe, though if anyone would have equipment that high grade, Geoff Emerick probably does.
Let's not get into the digital/analog debate, we all know the pros and cons of both systems, so let's assume we all know that a digital system at a sample rate of 44.1KHz just wouldn't reproduce the 56 and 57k at all, that sample rate can only theoretically reproduce frequencies as high as 22.05KHz (and only if the converters are any good... we'll move onto this).
However, a 192KHz sampling rate could, so again assuming someone had the speakers that could play a freq as high as 57k, a digital system with decent clocking (at least apogee or prism audio quality) could indeed process all those frequencies we are taking about. We just wouldn't hear them...
unless two frequencies within a critical bandwidth of each other are played, and then we have the same situation as with the above hypothetical analog system.
You are welcome to say that it all ends up on CD at 44.1khz and it would lose it. I think it would, unless the side effect of the 1KHz 'beating' does actually get recorded, but that is more of the debate which is open, because you'd have to test it, and the discussion is something of a headfuck as it already is! And of course, why would we even burn this test to CD?
I want to touch on
Nyquist theory for people, because I get the impression people don't fully understand it.
I'm sure you all know the gist of it - the highest potentially audible frequency, supposedly 20KHz, can only be properly represented with a sampling rate of twice that. If you aren't aware of that much, do and read a little more about it somewhere else.
But if this is the case, why would anyone record with a sampling rate above 44.1KHz?
Hands up, who records at a rate higher than 44.1KHz?In fact why isn't the sampling rate just 40KHz? Think of the sampling rate having a bit of a slope to it, like a low pass filter - 44.1KHz works because the 'slope' is higher, going up to 22.05KHz, rather than lower down in an audible range. This is with poor/common converters, you probably won't get this with Apogee (or above) quality. This is why, when we don't have that expensive quality, we use 48 or up to 96KHz, which people often describe as a more 'open' sound, because the theoretical LPF when using those sample rates is way higher and therefore does not affect the range we can hear, up to 20k.
If anyone says to you about how they use 96k sampling because the 'resolution' makes it sound better, they are actually wrong (stick with me), because 44.1 is technically as much resolution as you need to represent audible frequencies. 'Resolution' is an often cited reason for why higher sampling rates are better, and yes the resolution is higher, but it is not the reason people would naturally think at first, probably to do with presuming it is the same kind of thing as when an image has a lower resolution. It isn't at all. (There may indeed be a benefit with plug in processing at higher sample rates, but I am not qualified to answer that aspect of it).
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Okay, back to responding to quotes! I've covered everything but want to get specific.
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the beat may indeed be 1kHz but i tried it just there and couldn't hear a damn thing. my ultrasound sensor did however register a signal so there was an ultrasonic sound.
You may have realised after reading my post that you may need:
- Speakers that represent beyond 57KHz
- A sampling rate of 192KHz
- High quality converters
- Your ears exactly in line with the tweeters, since freqs are more direction as the get higer (a bass sub can go anywhere in the room, it is non directional, but higher freqs increasingly get more directional. Try a sine at something like 16KHz from only one speaker, listen to it of axis, then listen to it exactly on axis to the tweeter, it will be louder
And IMO there is no need to spend that kind of money of kit for a little experiment like this!
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Imagine taking something that is completely inaudible and then turning it off and on at 100 times per second. Do you think that this will miraculously make it audible at 100Hz - it wont.
Interesting example, because this is actually how beating works - the quick, repetitive phasing between the two signals IS turning it on and off because is nulls then sums at a new freq. BUT... to turn something on and off at 100hz just means something inadiuble is turned on and off, and remains inaudible. You are forgetting the summing part of the beat phenomenon.
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It looks like it's not possible if transmitting 51khz and 50khz [he means 56 and 57k] thorough the air to cause the 1khz harmonic as there is nothing to produce the harmonic. Unless the signals are being transmitted loud enough to cause the non-linear effects in the air. This of course could be bad for the ears. Another factor that could create this harmonic could be the speakers as they are also a non-linear system.
You mean 56KHz and 57KHz. I think the part of my post here answers where the beating effect is produced.
I can why you might think you need the >20KHz to be really loud to cause the beating at an audible volume, but they wouldn't have to be that loud - remember the equal loudness curve/fletcher munson curve? We are SUPER sensitive to sounds in the upper mid range, like 1KHz to 5KHz (roughly, depends on the person).
We would be able to pick up a sound at 1KHz easier than ANY potentially audible frequency. Consider this - imagine you have a bass sine at like 80Hz and a sine at 1KHz. If you have a mixer in front of you now get them up on two tracks, then try and match their apparent volume. The 1KHz fader would have to be a lot lower, because you are more sensitive to it. I heard that if that 1k sine actually had the same power as the bass note, it could kill you! Anecdotal of course, but the point is that a bass note has to have a LOT of energy just for us to hear it like normal. An upper mid range sound could sound just as loud as that bass note with very,
very little energy, such is our sensitivity to that range.
Now, I don't know for certain how much energy the 56 and 57k signals would need to produce enough energy for the 1K beating effect to be audible, but just remember that out of every feasible frequency, for example 0Hz to 1 million Hz(!!), the range of 1-5KHz(ish) needs the LEAST energy to it to be audible to us. Get me? Just for your consideration.
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Now to answer some of @boomtopper 's points on twitter:
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There was one guy on that thread saying he could hear the differance with a soldered joint?
Yes, this is a facinating story. Although it is not written on an academic, peer reviewed paper,
we should also give it the credibility it deserves, for the following reasons:This is an interview with
Rupert Neve, of course as in Neve, the effing better preamps and EQs etc of the entire history of recording. Rupert Neve, while talking to Fletcher (BTW, Fletcher is a very trusted and respected individual in the pro echelons of modern recording culture - he runs mercenary audio - though his credibility is irrelevant to this story, but perhaps of interest to you), recalls a story about
Geoff Emmerick, the most famous and emulated of engineers - you surely all know he engineered The Beatles, and pretty much invented many of the technique we use on a daily basis.
If
anyone had equipment good enough to playback these inaudible but somehow perceivable >20KHz frequencies, and trained enough ears, then it would have been this guy in this studio. And in turn, Rupert effing Neve agreed there was something different about these channels. And lo and behold,
they found there actually were transformers incorrectly fitted. Assuming the story is true, (and remember Rupert Neve was a first hand witness to this, and Fletcher is as trusted as it comes), then
this would be evidence that somehow, some people have perceived a difference when there was a +3db peak at 54KHz. I am not saying 'look, this is guarenteed proof of the concept', but it is a convincing demonstration of an effect we definitely do not know enough about.
We should admit that
science has not discovered everything to do with audio and the brains perception of it. We haven't by a long shot, and if you disagree, read a book on psychoacoustics, write down all the questions you think of along the way, then discover most of everyone's questions have not be researched let alone answered.
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It [the 1KHz side effect of 56 and 57KHz] is not a beating effect.
Yes it is.
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The bottom line is supersonic frequencies matter a lot less then you think
They don't particularly matter, according to our current understanding of science - I'm not trying to make out they matter even a percent of how much the audible range of 20-20k matters, but
I want everyone to accept we really don't know that they don't matter.QUOTE
the other way of creating this 1k sideband would be to play the 2 [56 and 57k] sines throught the air at very high volumes
This of course would be bad for the ears.
It wouldn't be bad for the ears, because the 56 and 57k sines are inaudible, so they wouldn't damage you. (as described ealiar, you wouldn't necessarily have to have those sines loud to get the 1k beating side effect. Maybe you would, but like I said before, probably not).
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This discussion on the effects of higher inaudible frequencies is very valid and overdue, in my opinion. They may be inaudible, but they may be
perceivable. At the other end of the spectrum, few would argue that sub 20Hz freqs are at least percievable. If a hypothetical 10Hz wave was coming out a speaker the size of a house, you wouldn't 'hear' a wave at 10Hz, but by god you would feel it. You might haemorrhage and die, such is the power! (infrasonics, the <20Hz range, is just as interesting and slightly more studied that ultrasonic sound).
Psychoacoutics is TOTALLY under-researched. Really, just because we can't hear a frequency above 20KHz (or lower, of course, because of ageing) doesn't actually mean that it's presence doesn't in some way affect our perception of it. In all my reading on the subject I have not come across conclusive proof (or any kind of proof) that we do not react to higher frequencies in some way. The topic of a side effect with beating that we have been discussing fascinates me, because it should remind us that their presence can have an audible effect.
What other tricks are lurking up there? Could research on this subject actually make sense for showing that HD audio
can actually have a measurable effect on quality/perception/air/space on a record?
Could this be the unique selling point for HD audio, something everyone had previously decided wouldn't make a difference since we can already get up to 20KHz with a regular CD player?
I urge anyone at uni with a dissertation coming up to study this, it would be a great topic to cover. There are gaps in our knowledge and perception of audio, and it may or may not be of our benefit to fill these holes.
May the discussion continue.
For my academic paper on 'Analysis, Testing and Discussion of Extreme Dissonance' which covers similar topics as here (but <20KHz), click here and download the relevant PDF.