Binaural beats - Page 1
Forum section: electronics / general

author: Peabody
author_rank: Super Contributor
timestamp: July 11, 2025, 05:52:45 pm
content: One of the hot new things is 40Hz stimulation, either vision or hearing, or both, to prevent dementia and other stuff. On the audio side what I see on Youtube is "binaural beats". This requires listening through headphones, with one channel outputting one frequency, and the other channel a different frequency that's 40Hz higher. So you could have 400Hz in the left channel and 440Hz in the right. They say this causes the brain to "hear" the difference frequency, which is 40Hz. I've tried it, and I don't hear anything but the two main frequencies - no difference frequency, and no sum frequency.I understand that the sum and difference will be produced, and can be heard, when the two waves are produced in the open air. That's how pianos are tuned. But I don't see any reason to believe that the brain does the same thing. I don't know why it would need to, or how it could.The advantage of binaural beats would be that the earphones don't actually have to produce a 40Hz tone to get you a 40Hz tone, or even lower frequencies for other therapies. They only have to produce higher frequencies.I can hear an actual 40Hz tone, which is the lowest E on the piano. No problem. And I can hear the beats of two different frequencies sounded together. But in the binaural beats setup, I don't hear that at all. So something here is definitely dodgy. It's either the concept of binaural beats, or it's my brain. Could be either.

author: Marco
author_rank: Super Contributor
timestamp: July 11, 2025, 06:00:38 pm
content: If it was at least the same ear it would produce 40 Hz.

author: edavid
author_rank: Super Contributor
timestamp: July 11, 2025, 06:08:37 pm
content: Quote from: Peabody on July 11, 2025, 05:52:45 pmMixing requires nonlinearity, and air is linear up to very high volume levels, so normal sound waves don't produce beats.Piano tuning with a tuning fork or other reference works by hearing that there are 2 separate frequencies instead of one, not by hearing a beat.(And of course piano tuners now universally use frequency counters instead of doing it by ear.)

author: TimFox
author_rank: Super Contributor
timestamp: July 11, 2025, 07:07:27 pm
content: Quote from: edavid on July 11, 2025, 06:08:37 pmIn a single ear, the mechanism converting sound to nervous stimulation is non-linear.There’s more to piano tuning than getting an exact frequency, since each note usually has three strings with individual tuning pegs. Due to non-linear details in the vibrations, the strings will suddenly and discontinuously lock to a single frequency as one string is tuned to approach another, and the gory details affect the attack and decay of the note. Substituting a counter for a fork can be confusing when the two strings are vibrating at different frequencies.

author: temperance
author_rank: Super Contributor
timestamp: July 11, 2025, 07:11:00 pm
content: QuotePiano tuners or musicians in general tune their instruments by listening to these beat frequencies.Here is an example:

author: BrianHG
author_rank: Super Contributor
timestamp: July 11, 2025, 07:16:45 pm
content: Quote from: Peabody on July 11, 2025, 05:52:45 pmThe truth is that the binaural beats has random results under tests. Specific patterns and times need to be met for a group of individuals to maximize a desired effect. One way and the effect may be positive, and the other way, the effect can actually be negative.There do exists mixed binaural beats processed music and/or AI generated music to help those with dementia, parkinson's and alzheimer's.The truth is that the right music alone would is whats doing the real work. Processing the music so that the bass drum replicates the binaural beat eerie effect is just quirky a way in to aid in user use/adoption.The classification of these kind of apps is known in the industry as 'Digital Therapeutics'.I would not rely on this tech, but if all else fails, for many, the music does some good.Apps which real-time generate the binaural encoded music offer the users that extra placebo to just enjoy the music playback.Example company:https://www.lucidtherapeutics.com/(I am not a doctor, I do not condone this technology.)

author: temperance
author_rank: Super Contributor
timestamp: July 11, 2025, 07:22:52 pm
content: I want to add a clarification about the beat frequencies you hear when a piano is out of tune. This has nothing to do with the linearity or non-linearity of your ears. What happens is that those sound waves are added together and you get interference. As such, you can't create binaural beats by using headphones.

author: floobydust
author_rank: Super Contributor
timestamp: July 11, 2025, 07:45:54 pm
content: One ear at 440Hz, another at 455Hz, you aren't going to "hear" a tone. What the ear hears and the brain's interpretation of that between ears, are not the same. It's not an op-amp.I have a few binaural meditation recordings, their heterodyne frequency is usually to create alpha, delta, theta brainwaves for concentration, alertness or sleep and relaxation etc.I can certainly feel it and see it on a FFT spectrum analyzer in the media player, as a large amplitude (music tone) carrier spike. Not a sine wave of course.Best results for me areDr. Jeffrey Thompson products.I find there is a difference and benefit.It was a "fad" decades ago and quite expensive for the CD's e.g. Holosync which is quite a blast to try.Now some companies add subliminals, which I have no idea if these do anything other than be a marketing gimmick. It's become a massive industryThere is also binauralstimulation(not beat frequency) sound alternating right-left ear for EMDR and PTSD sufferers.Mark Grant MAAustralian shrink is well known for his work.I mean just try the stuff. Most products seem like garbage where the content creator doesn't know what they are doing. You end up listening to annoying heterodyning sounds that kind of give you a headache and nothing more.

author: edavid
author_rank: Super Contributor
timestamp: July 11, 2025, 07:46:31 pm
content: Quote from: temperance on July 11, 2025, 07:22:52 pmAs I said, this is not true. Sounds in air add linearly, so there is no interference.

author: floobydust
author_rank: Super Contributor
timestamp: July 11, 2025, 07:56:31 pm
content: I read this new product description... uh beyond dodgyIt's "hypothesised" wow“IOTA 1.0” is an innovative album at the frontier of brainwave research, exploring frequencies beyond traditional brainwave states. It introduces IOTA 1 and 2, hypothesized to align with Earth’s biosphere rhythms, a concept supported by the recent discovery of Earth’s 26-second “Heartbeat.” Designed for daily listening, “IOTA 1.0” offers a transformative auditory experience, aiming to deepen the listener’s connection with the Earth and expand consciousness. This album is a unique tool for meditation and personal exploration into new realms of science and awareness."

author: TimFox
author_rank: Super Contributor
timestamp: July 11, 2025, 08:01:08 pm
content: This was worked out by H Helmholtz, and can be found in his magnum opusOn the Sensations of Tone as a Physiological Basis for the Theory of Music4th German edition (1877),2nd English edition by A Elllis (1885)pdf:https://ia801302.us.archive.org/6/items/onsensationston00unkngoog/onsensationston00unkngoog.pdfSee chapters VII and VIII about tones (combinations of simple sine waves) and beats, respectively.In discussions of consonance and dissonance, he emphasizes the beats between overtones of the tones found in a chord.

author: tszaboo
author_rank: Super Contributor
timestamp: July 11, 2025, 08:13:19 pm
content: Hearing is weird. For example, you can hear direction with just one ear. Or your brain does fill in a lot of things, you can 100% hear an instrument in a song you remember, even if it is not there. Same goes typically for vision, color perception has similar weirdness, where objects in the background only have color if you looked at it before.That being said, I don't believe in binaural beats having any benefit. Listen to some binaural recording of music though, that's really cool. There is an album from Pearl Jam, I highly recommend it.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 11, 2025, 08:20:08 pm
content: Regarding beat frequencies: I'm not sure about the mechanism that produces them (non-linearity and all), but you can definitely hear them when two notes are played simultaneously.I play violin, and when tuning it one plays two adjacent strings (tuned in fifths) against each other. It's not terribly strong, but you can definitely hear beat frequencies as the string being tuned approaches a perfect fifth against the other string. (Same with guitar, where (most of) the strings are tuned in fourths.)So where does the non-linearity come in here?

author: TimFox
author_rank: Super Contributor
timestamp: July 11, 2025, 08:20:14 pm
content: Quote from: tszaboo on July 11, 2025, 08:13:19 pmIn the Helmholtz reference, he discussed "implied fundamentals", which are frequencies not actually present in the sound, but are inferred from the harmonic content of the tones actually in the sound (e.g., multiple organ pipes).Apparently, this useful device was discovered by organ makers ("mixture stops") before the effect was understood mathematically.When stereophonic recording was new, there was a movement for true binaural recording (putting two microphones inside a dummy human head to get the binaural effect), but it did not catch on commercially because of the need for headphones.I agree that the binaural effect, properly done, is way cool.

author: edavid
author_rank: Super Contributor
timestamp: July 11, 2025, 08:23:58 pm
content: Quote from: Analog Kid on July 11, 2025, 08:20:08 pmIt has to be coming from the violin body and/or the strings themselves.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 11, 2025, 08:40:20 pm
content: Quote from: edavid on July 11, 2025, 08:23:58 pmThat makes sense. The behavior of the vibrating plates (top and back) of a stringed instrument is highly complex, as shown byChladni patterns(powder sprinkled on the plates as they are excited by vibrations).

author: temperance
author_rank: Super Contributor
timestamp: July 11, 2025, 08:54:37 pm
content: QuoteI already answered that. It's interference. The two signals add together and at some points in time they cancel which is called destructive interference and at some points in time they add up which is called constructive interference. What you hear is the envelope of two signals added together.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 11, 2025, 09:01:11 pm
content: Quote from: temperance on July 11, 2025, 08:54:37 pmYes, I understand that.What I don't get is the oft-repeated statement that this requires some sort of nonlinearity to occur.It sounds like you're saying that this is not the case, that two signals can simply combine to produce sum and difference frequencies through constructive/destructive interference.This is my instinctive belief as well, that this will occur despite the absence of nonlinearity.But is this true? Must there be some non-linear element in the sound path for this to occur?To put this into electronic terms, what happens if one simply mixes two different-frequency signals like so?No nonlinearity here. But don't we get beat frequencies by virtue of constructive/destructive interference here as well?Or do we need a true mixer for that to happen?

author: TimFox
author_rank: Super Contributor
timestamp: July 11, 2025, 09:21:17 pm
content: Attached is a simple graph showing the superposition of two equal magnitude signals at 1000 and 1100 Hz.The top graph shows both sine waves individually on a common set of axes.The middle graph shows the (linear) sum of the two sinusoids: note the obvious effect with a period of 10 msec (100 Hz) in the instantaneous linear values.This is an example of the "interference" mentioned above.The lower graph shows the magnitude of the sum as a function of time.Now, the lower graph could result from 2nd-order non-linear distortion of the composite signal, but to the extent that the ear is sensitive to magnitude it would sense the lower graph along with the actual signal.Of course, practical instruments not only have non-linear distortion in the bridge, etc., but generate complex waveforms that include the integer harmonics of the fundamental.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 11, 2025, 09:40:38 pm
content: Thanks for that.One thing I don't understand:Quote from: TimFox on July 11, 2025, 09:21:17 pmWhat exactly does that mean?One interesting thing strikes me: if you treat one of the constituent frequencies (1.0 or 1.1 kHz) as a carrier wave, if you then "demodulate" the middle wave by rectification and filtering out the "carrier", you'd end up with the 100 Hz difference wave, yes?Not sure if that is meaningful or not.Wait: is that bottom waveform the absolute value of the middle one? Sure looks like it.

author: TimFox
author_rank: Super Contributor
timestamp: July 11, 2025, 09:45:10 pm
content: Quote from: Analog Kid on July 11, 2025, 09:40:38 pmThe usual meaning of magnitudeMof an amplitudeAthat goes positive and negative:M(t) = [A(t)2]1/2which is positive-definite. For a real-valued function, this is also the usual absolute value.

author: Peabody
author_rank: Super Contributor
timestamp: July 11, 2025, 10:05:19 pm
content: I just had a long conversation with ChatGPT, which assured me that some people can indeed "sense" the 40Hz pulses in binaural beats, but others cannot. Apparently I am one that cannot. We agreed that if I can't sense the 40Hz in any way, it might be better to dump binaural beats in favor of supplying a pure 40Hz tone, which of course Audacity can provide with good speakers, and which I can easily hear.I want to emphasize that based on specific instructions on Youtube, my understanding of binaural beats is that each ear must be provided with only one of the tones, with no mixing. So if you listen only to the right headphone, you hear 400Hz, but if you listen to the left, you hear 440Hz. I still don't understand how the 40Hz could be "heard" or sensed in any way by the brain, and I suspect ChatGPT is just buying into the abundant woo on this subject. But I could be wrong.Anyway, I would think that even if the 40Hz beats are sensed in some way, a plain 40Hz tone to begin with would be much stronger and more effective than the dim beats.Thanks very much for all the comments.

author: tszaboo
author_rank: Super Contributor
timestamp: July 11, 2025, 10:14:39 pm
content: Some headphones and amplifiers might be better at it. Most cheap ones share a ground lead, and they have low impedance, so a phone or a "CD player with 2 AA batteries" can drive it. If the wire is 2 Ohm and the headphone is 32, you get 2/32 crosstalk, or 3%. Which doesn't sound like a lot. But then again, hearing is weird, logarithmic, making it worse.I think I tried it a few years ago, but I only remember hearing something best described as "clicking"

author: floobydust
author_rank: Super Contributor
timestamp: July 11, 2025, 11:18:07 pm
content: It's much lower frequency for useful brainwave entrainment. 40Hz seems way up there.I notice the effect the most with Holosync- Dive & Immersion feels like your head is being squished. You can feel it alright. Alpha to Delta; or 8-12Hz down to 0.5-4Hz it's inaudible.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 12:19:14 am
content: Continuing with the electronic version of beat frequencies:Can someone tell me the difference between the outputs of these two circuits?The first one being just a simple summer, the second a proper (nonlinear) mixer.Let's assumef1 = 1000 Hz andf2 = 1100 Hz, as in Tim's graphs above.Will we see sum and difference frequencies from both circuits?This is something that's been bothering me for a long time now ...

author: temperance
author_rank: Super Contributor
timestamp: July 12, 2025, 12:41:21 am
content: QuoteSearch google for images with "beat frequencies".The difference I think you are after is the difference between mixing signals and summing signals like in the example discussed here. Those are not the same operations.Summing signals: when you add two signal ω1 + ω2 and when those two frequencies are very close to each other, you get something which looks like an amplitude modulated waveform. The envelope of this waveform is ω1 - ω2.Mixers are different things. They don't sum two signals together but instead multiply the instantaneous values of two signals. You can basically take any circuit which can multiply. You can for example take two logarithmic amplifiers and sum their outputs to perform multiplication. The problem with this method is speed. But multiplication can also be performed by "exploiting" the exponential IV characteristic of a PN junction. How multiplication is performed with those exponential IV characteristics is more difficult to explain, and goes into the territory of power series and trigonometry.An explanation without going into the details of power series and trig functions and a demonstration of what a mixer does can be found here:If you like power series and trigonometry, this presentation shows how non-linear devices perform multiplication.:https://www.ece.nus.edu.sg/stfpage/eleguoyx/EE5403/EE5403%20Lecture%201%20mixer%202007.pdf

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 01:10:29 am
content: Sorry, I'd prefer anactual explanationto a YouToob video.Thanks anyhow.

author: edavid
author_rank: Super Contributor
timestamp: July 12, 2025, 01:47:05 am
content: An ideal summer doesn't change the spectrum of the signals. You can prove this by comparing the sum of the FFTs to the FFT of the sum. They will be the same.

author: TimFox
author_rank: Super Contributor
timestamp: July 12, 2025, 02:08:11 am
content: Quote from: Analog Kid on July 12, 2025, 12:19:14 amThe first diagram (summer) does not add frequencies to the two frequencies applied.The second diagram (multiplier) ideally outputsonlythe sum and difference frequencies.As an exercise, you can prove the latter using the trigonometric identitysin(a) x sin(b) = (1/2)[ cos(a-b) - cos(a+b) ]

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 02:10:30 am
content: Can you explain the difference between the outputs of those two circuits I posted?And please, no Fourier math. Yes, I understand basically how the series works (e.g., add together enough odd harmonics of a sine wave and you get a square wave), but the math makes my head hurt.

author: TimFox
author_rank: Super Contributor
timestamp: July 12, 2025, 02:14:05 am
content: You don’t need Fourier for this question, only the trig identifies.He’s referring to Fourier analysis (or transform), not Fourier series.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 02:14:58 am
content: Quote from: TimFox on July 12, 2025, 02:08:11 amYou mean to say the summer willnotoutput sum and difference frequencies in addition to the two input signals?Don't you get sum and difference frequencies just from constructive and destructive interference?Using your earlier graphs, your second graph shows a simple summation of the two signals, correct?Doesn't that signal contain sum and difference frequencies?

author: TimFox
author_rank: Super Contributor
timestamp: July 12, 2025, 02:18:24 am
content: Quote from: Analog Kid on July 12, 2025, 02:14:58 amNo, the second graph shows interference causing maxima and minima in time, but there are only two lines in the frequency spectrum, which I didn’t graph.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 02:23:32 am
content: Quote from: TimFox on July 12, 2025, 02:18:24 amSo does the summer basically just output a distorted version of both input waves? How would you describe its output?

author: TimFox
author_rank: Super Contributor
timestamp: July 12, 2025, 02:31:21 am
content: Quote from: Analog Kid on July 12, 2025, 02:23:32 amThe output of the summer as a function of time is merely the sum of the two sine waves, each of which is a line (single frequency) in the frequency spectrum.An ideal summer (e.g. two resistors) is linear and does not introduce distortion products.A real analogmultiplieris less ideal and will introduce small distortion products and fundamental feed-through along with the ideal sum and difference frequencies. If you model the multiplier with a polynomial inaandb(my earlier notation), you can calculate the distortion product frequencies using high-school math: algebra and trig identities.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 03:01:26 am
content: Thanks; I think I'm getting it now.One last thing: taking your summed waveform and connecting the wave tops:is it possible that even though this difference frequency (100 Hz) doesn't actually exist in the summed waveform, that the ear might be able to perceive it? Thus you would kinda-sorta have beat-frequency generation without nonlinearity.(forgive the poor curve fitting)

author: TimFox
author_rank: Super Contributor
timestamp: July 12, 2025, 03:32:34 am
content: Yes: the ear and its connection to the brain are not an oscilloscope.Nerves cannot have a bandwidth of 20 kHz, yet we can perceive frequencies that high before listening to excessive rock music.An over-simplified model for a narrow-band ear system would be a filter with a passband from 950 to 1150 Hz (for the system in my graphs) followed by an AC voltmeter. The voltmeter would show a slow variation (100 Hz) like what you sketched into my graph. This is not a linear system, more like the AM detectors discussed elsewhere.My understanding of the actual ear (from what I remember from a lecture 50 years ago) is that the ear contains a thingy whose resonant frequency varies along its length. A bundle of nerves (cable?) has endings along that thingy that map the frequency (encoded by position there) to an appropriate locations in the brain. This would be an ensemble of filter-voltmeters analogous to the single-channel one in my simple system.Another lecture (from 30 years ago) had early functional MRI data that seemed to indicate a constant slope in physical location within the brain in mm per octave (log frequency response). I don’t know the current state of research on that phenomenon.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 03:43:39 am
content: Quote from: TimFox on July 12, 2025, 03:32:34 am

author: temperance
author_rank: Super Contributor
timestamp: July 12, 2025, 10:41:44 am
content: QuoteSome concepts require effort to understand. Instead of investing your own time, you repeatedly ask the same question until you get an answer you find satisfactory. I find that somewhat arrogant toward others who put their time and effort into answering your questions. You don't even bother to try. You dismiss explanations instantly, saying something like, "I don't understand this, and I want a different explanation, and I also don't like videos." Essentially, you're asking people to invest their time to accommodate your needs when answering your questions. This certainly isn't the first time I've seen this from you. Don't you think it should be the other way around? You put in some effort into understanding what people wrote, just as people put effort into answering you.I think I remember you wrote some time ago that you were good with mathematics. The interesting part about why mixers can be made with non-linear devices is in the PDF I linked to. Some power series and some trigonometry... Nothing fancy.

author: temperance
author_rank: Super Contributor
timestamp: July 12, 2025, 10:54:22 am
content: QuoteRepeat: MIXING is the multiplication of the instantaneous values of signals, which isNOT THE SAMEas adding signals. I wrote that literally in my earlier post including the most basic mathematics namely addition and multiplication. But you just ignore that and keep on repeating the same question.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 06:58:05 pm
content: Quote from: temperance on July 12, 2025, 10:41:44 amI think you misremember; I probably wrote that I wasnotgood with mathematics. Certainly not bragging about something I am admittedly deficient in.As to the rest of your critique of me, will you please kindly just fuck off? I don't need your chiding and needling about the way I go about trying to get answers to questions here.

author: temperance
author_rank: Super Contributor
timestamp: July 12, 2025, 08:13:10 pm
content: QuoteDear Sir, I don't know who you are but unlike you, I have been very polite. Repeating your question over and over until someone might come up with an answer you might be able to understand instead of putting some effort into understanding what people carefully craft together to answer your question is very unpolite. People even have to formulate answer the way you want them to be formulated. That sir is beyond rude, and here is why:Effort 1: To answer your question, one must identify which part you have trouble with. So I must understand what you ask.Effort 2: Write an answer which tries to clarify the parts required, and find some written or video resources. How much time do you think goes into that?Your effort: 0.000 you don't even try to understand what people write.Do you still think you can tell me to kindly just fuck off?EDit: I forgot to mention you have the last word in this. I will just kindly fuck off, obeying your orders.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 08:45:36 pm
content: I'll just point out to you that the reply immediately following one of my questions that you so object to (reply #36 by Tim Fox) did, in fact, answer my question quite nicely. Perhaps you missed that.

author: tszaboo
author_rank: Super Contributor
timestamp: July 12, 2025, 09:14:43 pm
content: Quote from: temperance on July 12, 2025, 08:13:10 pmIDK if you noticed, but you are arguing with someone who has the temper (pun intended) of a 4 year old and the technical knowledge as well (which is only an issue if you have that temper, we all started somewhere). He found this forum, blurped 2000 comments in off topics in a week, and made zero actual technical contribution to this forum. Just let him do this temper tantrums...

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 09:18:47 pm
content: Quote from: tszaboo on July 12, 2025, 09:14:43 pmBullshit. I may not be the top contributor here--far from it--but if you care to check I have contributed more than just opinions and complaints.You too can just please kindlyfuck off.Yes, that's rude. Intentionally so. So sue me.

author: ejeffrey
author_rank: Super Contributor
timestamp: July 12, 2025, 10:18:03 pm
content: Quote from: Analog Kid on July 11, 2025, 09:01:11 pmEnvelope detection is non-linearity. In fact, the entire concept of "loudness" is intrinsically non linear because the average signal is zero.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 10:24:05 pm
content: Quote from: ejeffrey on July 12, 2025, 10:18:03 pmI don't get that (bolded part); could you please explain?Do you mean the average signalover time? over what period?And how does this make loudness "intrinsically nonlinear"?Thanks in advance for an explanation.

author: TimFox
author_rank: Super Contributor
timestamp: July 12, 2025, 10:49:11 pm
content: Quote from: ejeffrey on July 12, 2025, 10:18:03 pm"Loudness" is a term related to human perception, and it is loosely based on the RMS value, not the mean, of the signal.As a measurement, it is measured in "phons".https://www.merriam-webster.com/medical/phonThe non-logarithmic unit is the "sone".

author: vk6zgo
author_rank: Super Contributor
timestamp: July 12, 2025, 11:14:55 pm
content: Quote from: edavid on July 11, 2025, 06:08:37 pmBack in the day, I worked at a Broadcast Transmitter site, which had two MF & two HF transmitters in a large hall.Each of those had an individual wall mounted monitor speaker, fed by the audio output of the modulation monitor associated with that transmitter.We would, before handing them over to the studio, run the transmitters with 440Hz lineup tone, derived from several different audio oscillators.These were not locked to each other so they were at slightly different frequencies.Moving along the hall there were places where the sound level between adjacent speakers were equal & "beat notes" were distinctly audible.The required non-linearity is provided by our ears.

author: ejeffrey
author_rank: Super Contributor
timestamp: July 12, 2025, 11:23:29 pm
content: Quote from: Analog Kid on July 12, 2025, 10:24:05 pmBasically yes. When you hear a loud tone at 1kHz vs quiet, you don't perceive "starts at the background pressure, pressure increases for 500 microseconds, returns back to average, then decreases below average, then repeats." You hear a "steady" tone even though it's oscillating 1000 times a second. We perceive the higher amplitude signal as louder.The normal mathematical way to treat this is with the mean squared amplitude. That's both because it's mathematically convenient and it's the formula for power/energy in a linear system. But any response that qualitatively matches your idea of loudness will do: such as squared, absolute value, peak detection.In terms of the averaging time, somewhere around 10-15 Hz is where our perception shifts from "rhythm" to "pitch." So roughly 100 ms. But nothing in psychoacoustics is exact.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 11:35:20 pm
content: OK, thanks; but what I still don't understand is your statement that "the average signal is zero". You didn't explain that part.How is this true, and how does this affect the perception of loudness?

author: ejeffrey
author_rank: Super Contributor
timestamp: July 12, 2025, 11:46:52 pm
content: Quote from: Analog Kid on July 12, 2025, 11:35:20 pmFor any sine wave the average value is zero. It has equal parts positive and negative. So the force on your ear drum is half the time pushing inward and half the time pushing outward.So if you try to make an averaged signal out of the instantaneous pressure and you only do linear averaging the result would be zero regardless of signal. So that's no good as a measure for loudness or intensity.It's not just sound. If you look at an AC coupled sine wave on an oscilloscope you will immediately identify a large or small amplitude signal. You will say the large amplitude signal is "stronger" even though the average voltage is zero.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 12, 2025, 11:50:19 pm
content: Ah, so.So in order to measure loudness you'd need to do something nonlinear, say (f'rinstance) rectifying the signal and integrating its amplitude, yes?. Am I getting warm here?

author: vk6zgo
author_rank: Super Contributor
timestamp: July 13, 2025, 01:22:44 am
content: Quote from: Analog Kid on July 11, 2025, 09:01:11 pmIf you look at that output with an oscilloscope, you will see two separate tones, but if you then use the combined output to feed a set of headphones, you will hear beat notes, because your ears are non-linear, & must be, to survive in the real world.In another part of my miss-spent youth, I worked at Wyndham, a "cow-town" in Western Australia's tropical North.For communications, we were at the far end of a very long "pole route", which ultimately joined us, along with other towns along the way, to Geraldton 2,914.7km away (road distance, that the pole route closely paralleled).In the "Wet" it was not unusual for poles to get washed out due to flooding, so we had backup in the form of several Independent Sideband(ISB) HF transmitters & receivers, linking to Derby, the next sizable town.(566 km away).ISB systems place different information on the Upper & Lower Sidebands of a transmitted RF signal.The traditional way to do this, was to transmit a Suppressed Carrier, along with the two Sidebands & use an ISB adaptor to lock a receiver to that carrier at the receiving end, or to have a "designed from scratch" ISB receiver.The Suppressed Carrier meant a substantial reduction in wasted power, but the EEs still weren't happy, so when a manufacturer came up with a system that could operate with a "fully Suppressed Carrier", they decided to buy a bunch of them.These relied upon very stable oscillators in both the transmitter & receiver, but sadly, they were not "very stable", & callouts to retune them were an everyday affair.The standard way to tune the receivers was for the transmit site to input the same tone to both Sidebands, & at the receive end to tune the receiver for a beat note between the two Sidebands.The separate audio outputs from the two Sidebands were available at a jackfield, so the tuning procedure was to simply parallel those outputs & feed them to a pair of headphones.As the receiver was tuned, the tones would change, until at the point where the tuning was very close, an audible beat would occur.Further fine adjustment would bring them to the point where the beat frequency was so low as to be inaudible.

author: ejeffrey
author_rank: Super Contributor
timestamp: July 13, 2025, 01:33:13 am
content: QuoteYes. But it doesn't even have to be an identifiable process. In the oscilloscope example, if you produce a pair of sine waves at 440 and 445 Hz you will be able to see the "beat note" clearly on the screen. Nothing about the oscilloscope is non-linear. It is your interpretation that is non-linear.Now take the two tones at 440 and 445 Hz and display them on separate oscilloscope channels. The signals are the same as before but there is no interference and you don't see an obvious beat note.

author: vk6zgo
author_rank: Super Contributor
timestamp: July 13, 2025, 01:57:51 am
content: Quote from: ejeffrey on July 13, 2025, 01:33:13 amIf you trigger to one of the tones, you can watch the other one drift across the screen at a rate determined by the frequency difference.As nothing is fair in the real world, it is also phase dependent, which will become dominant after the frequencies become very close.

author: TimFox
author_rank: Super Contributor
timestamp: July 13, 2025, 03:33:04 am
content: Quote from: ejeffrey on July 12, 2025, 11:46:52 pmYes, the average or mean value of a sinusoidal signal is the DC level, which is not part of the acoustic loudness.

author: Peabody
author_rank: Super Contributor
timestamp: July 13, 2025, 04:00:15 am
content: If two frequencies are multiplied together, and the result fed into a spectrum analyzer, I assume you would see the original frequencies plus the sum and difference. The sum and difference frequencies would be physically present. I think that would be the case for AM modulation, for example, where the carrier is multiplied by the audio signal.But if you simply summed the two frequencies and fed that into the spectrum analyzer, would you see anything other than the two original frequencies? My guess is you would not. Your ears would hear amplitude beats, but not as a separate tone.Is that even close to right?The interest in 40Hz sensory stimulation derives from an MIT study on mice where an actual 40Hz tone substantially reduced the progression of dementia in mice that were genetically prone to dementia. The question is whether the mixing of two higher tones that are 40Hz apart - mixing in any way - can produce the same result as a 40Hz tone. Moreover, if the two signals are kept separate and just one fed into each ear (binaural beats) , does any mixing take place at all? In that latter case, I can't hear any difference tone at all, which makes me think that method is dodgy. AI says I'm wrong, that some people "hear" or "sense" the difference, but I think AI is dodgy, so there.

author: fourfathom
author_rank: Super Contributor
timestamp: July 13, 2025, 04:55:44 am
content: Quote from: Peabody on July 13, 2025, 04:00:15 amAlmost correct. In AM the carrier is multiplied by the (audio signal + offset), where the offset is the peak value of the audio. So the normalized audio modulation signal ranges from zero to one (it never goes negative). What you describe is actually Double Side Band modulation.For radio AM, you need a nonlinear detector to recover (and hear) the audio modulation. But this is not what is happening when we hear audio beat-notes. In that case we have twoaudio-frequencysignals of slightly different frequencies that are linearly summed. As has been mentioned up-thread, these add, and as the phase relationship shifts from zero degrees (constructive) through 180 (destructive) and back to 360/0 (constructive) the signal level varies from 1+1 to 1-1 and back to 1+1. This happens to look exactly like an audio frequency carrier being AM modulated by the a signal at the frequency difference. This is the beat note.But in this case for all practical purposes our ears are linear, so there is no detection or sum + difference signal. Instead we hear the signal level vary at the beat note rate and while we might associate this with (say) a 3 Hz signal this is just a brain function. What we actually hearing is the amplitude swelling and fading.As the beat note frequency is increased we eventually no longer hear the beats as amplitude variations but we do hear the two different tone frequencies.In some cases ears can be nonlinear but I don't know the mechanism. In my case though, I have fairly strong constant tinnitus (high frequency ringing due to my mis-spent youth as a rock bass player). When I hear actual strong high frequency sounds I can sometimes hear the difference products -- as the external frequency increases the nonlinearity in my inner ear creates a decreasing-frequency difference tone.

author: Peabody
author_rank: Super Contributor
timestamp: July 13, 2025, 01:41:27 pm
content: Quote from: fourfathom on July 13, 2025, 04:55:44 amThanks very much for that explanation. So a spectrum analyzer would not show a 3Hz signal as being present?And if a real 40Hz tone stimulation produces some benefit in the brain, would that benefit also be produced by:1. linear summing of higher tones 40 Hz apart, with the result played through one speaker (beats)2 multiplying the two frequencies and playing through one speaker (actual difference tone)3. playing the two tones separately to each ear through earphones ("binaural beats")It seems to me #2 is the only one with any chance of producing the same benefit as a 40Hz tone, and even then it will be weaker. And for those who, unlike me, claim to "hear" or "sense" the difference frequency in #3, I wonder what mechanism would produce that result. Maybe bone conduction or something like that.

author: TimFox
author_rank: Super Contributor
timestamp: July 13, 2025, 03:14:40 pm
content: The term “interference” has come up in the discussion of beats in a linear medium.In this case, the interference is in the time domain.In other cases, such as optical diffraction or antenna patterns, the interference is a function of angle.In these cases, although we speak of constructive and destructive interference, there is no loss of energy, just a re-direction or re-arrangement, giving peaks and valleys in the result.In my graphs posted way above, note that the sum of two sinusoids, each with peak value 1, gives a result with amplitude peaks at 2 (constructive) and valleys at zero (destructive), repeating at a time equal to the reciprocal of the frequency difference (1100 - 1000 = 100 in my example).This variation in amplitude is audible, even though a spectrum analysis (or Fourier transform) does not contain a component at that difference frequency.

author: paul cotter
author_rank: Regular Contributor
timestamp: July 13, 2025, 03:41:35 pm
content: It is many, many decades since I did this stuff but I do remember the response of the human ear being described as logarithmic and this would clearly be a case of non-linearity. Certainly on tuning a guitar the beat notes are quite obvious.

author: TimFox
author_rank: Super Contributor
timestamp: July 13, 2025, 05:22:38 pm
content: There is a general law in biophysics that the perception of stimuli (including hearing) is logarithmic, which makes sense given the very wide range of physical intensity that hearing (for example) can handle (> 120 dB).See general discussion about the “Weber-Fechner Law”.Perception includes the actual physical response of the relevant sense organ and the further processing in the appropriate cortex.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 16, 2025, 11:18:10 pm
content: Quote from: vk6zgo on July 13, 2025, 01:22:44 amOK; I started working on a very rudimentary virtual oscilloscope, something I've been wanting to do for a long time.This testbed includes a two-tone sine wave generator that mixes the signals (simply adds them together, averaging the sum). Here's a screenshot:I don't see two separate tones here; just one wave that has a rising and falling envelope.What did you mean when you said that "you will see two separate tones"?(I have an actual oscilloscope, but no signal generator, let alone two of those.)BTW, you'll notice that the two tones are 1Khz and 1.2KHz; that's because I tried 1.1KHz (as in Tim Fox's example) but couldn't get it to work. I think it's because of the floating-point arithmetic I'm using, where I need to calculate the number of samples to output for each frequency as an integer, and there's some kind of cumulative rounding error when the difference between the two frequencies gets too small. Other than that it works fine. (Written in assembly language for Win32.)

author: tggzzz
author_rank: Super Contributor
timestamp: July 17, 2025, 09:11:55 am
content: Quote from: edavid on July 11, 2025, 06:08:37 pmThe ear-brain combination is one of the most non-linear "devices" I'm aware of - in any and every dimension. If it wasn't then audio compression would not be possible.

author: tggzzz
author_rank: Super Contributor
timestamp: July 17, 2025, 09:24:13 am
content: Quote from: TimFox on July 12, 2025, 10:49:11 pmVeryverylooselyhttps://en.wikipedia.org/wiki/Equal-loudness_contour

author: TimFox
author_rank: Super Contributor
timestamp: July 17, 2025, 02:35:03 pm
content: Note that the “phon” is defined to agree with “dB SPL” at 1 kHz, but then varies with frequency from the physical value according to the psycho-acoustic response of human perception.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 17, 2025, 06:04:08 pm
content: So Tim, can you tell us why I don't see the two tones on my fake oscilloscope screen shown above like that other person said I should be able to see?

author: TimFox
author_rank: Super Contributor
timestamp: July 17, 2025, 06:51:44 pm
content: Tones:If you sum two sine waves, you will see two "tones" or "lines" in the frequency domain, when using a spectrum analyzer.What you see on an oscilloscope is in the time domain.If your oscilloscope supports a Fourier transform, you can analyze the time-domain data to get the frequency domain, and should see two lines in that domain.The structure of the human hearing system is similar to a Fourier analysis, responding to tones, since the nerves do not have an inherently high bandwidth for transmitting stimuli to the brain, and a bundle of nerves is required to span the spectrum of hearing.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 17, 2025, 07:32:01 pm
content: Quote from: TimFox on July 17, 2025, 06:51:44 pmSince my "oscilloscope" lacks a Fourier transform and is not a spectrum analyzer, I cannot see two distinct tones. So that earlier statement was wrong.

author: TimFox
author_rank: Super Contributor
timestamp: July 17, 2025, 09:14:04 pm
content: Quote from: Analog Kid on July 17, 2025, 07:32:01 pmFor the simple problems of the sum of two sine waves and the product of two sine waves, fancy Fourier-transform math is not required.Only "trigonometric identities" need to be used.Although you scoff at Wikipedia, its article on these identities is straightforward.A classic reference (excerpted from the Rubber Bible) is D ZwillingerCRC Standard Mathematical Tables and Formulae, CRC Press 2012, pp 404 to 410 (especially sections 6.5.3 to 6.5.6.5.14)

author: Analog Kid
author_rank: Super Contributor
timestamp: July 17, 2025, 09:58:38 pm
content: Quote from: TimFox on July 17, 2025, 09:14:04 pmAlright, fine. OK if I come over to your house and peruse that volume?

author: TimFox
author_rank: Super Contributor
timestamp: July 17, 2025, 10:08:44 pm
content: Quote from: Analog Kid on July 17, 2025, 09:58:38 pmNo: I'm on vacation next week. I recommend you buy it, it's an encyclopedic reference.Cheaper: look at online used book stores for an older edition of the Rubber Bible, or download the pdf and print only the good pages.https://mathguy.us/BySubject/Chemistry/CRC_Handbook_of_Chemistry_and_Physics_97.pdfMeanwhile, try the Wikipedia article: nothing wrong with it.

author: Analog Kid
author_rank: Super Contributor
timestamp: July 17, 2025, 10:10:46 pm
content: Quote from: TimFox on July 17, 2025, 10:08:44 pmThanks, but that's a no. (TheRubber Bible, really?)

author: TimFox
author_rank: Super Contributor
timestamp: July 17, 2025, 10:11:45 pm
content: Quote from: Analog Kid on July 17, 2025, 10:10:46 pmYes: the original publisher name was The Chemical Rubber Company (vendors of fine rubber hoses for chemistry labs).See my revised answer above for a cheap alternative.Older copies of theHandbook of Chemistry and Physicsare useful, since later editions may have removed items, since the book is already too damned thick.At my job, I once needed the physical properties of Freon 12, along with the more modern refrigerants.My copy was after Freon 12 was banned, and did not include those properties, nor did the DuPont website, since they no longer made it.My coworker in the next office had an older copy from his college days, which predated the ban, and I found the information there.

author: vk6zgo
author_rank: Super Contributor
timestamp: July 18, 2025, 12:21:59 am
content: Quote from: Analog Kid on July 17, 2025, 07:32:01 pmIf you input the two tones to one channel of ananalogoscilloscope, you will see a constantly changing display, as over time, the two tones reinforce or cancel depending upon the instantaneous levels & timing of those signals.I have never done such a test with a DSO, but am fairly sure that a fully featured one would give the same result, unless you specifically required it to give a display like your "virtual" 'scope.

author: TimFox
author_rank: Super Contributor
timestamp: July 18, 2025, 02:47:59 am
content: The graphs I showed in my post above were done by simply generating two columns in an Excel spreadsheet for each of the two frequencies (1000 and 1100 Hz), vs. time in the first column.From that, I computed the sum signal and the magnitude in two more columns.The graphs were generated directly from those columns and represent what an oscilloscope would show for a single sweep (that happened to start when both sinusoids started from zero).

author: BrianHG
author_rank: Super Contributor
timestamp: July 18, 2025, 10:51:52 pm
content: See my post here:https://www.eevblog.com/forum/chat/fun-for-nerds/msg5982747/#msg5982747There is a section describing what happens when you mix 2 sine waves.

author: tggzzz
author_rank: Super Contributor
timestamp: July 18, 2025, 11:30:11 pm
content: Quote from: BrianHG on July 18, 2025, 10:51:52 pmThat's "mix" as in "add", i.e. the audio engineer's operation.Not "mix" as in "multiply", i.e. the radio engineer's operation.

author: fourfathom
author_rank: Super Contributor
timestamp: July 18, 2025, 11:43:47 pm
content: Quote from: vk6zgo on July 18, 2025, 12:21:59 amA digital scope will give the same display as long as you set up the triggering and sample rate appropriately. Same for triggering with an analog scope. Analog Kid's virtual scope is also correctly displaying an additive audio beat, just the same as you would see with a single-sweep on any other scope.And as Tgqzzz noted, "mixing" has different meanings in different domains. A sound-tech's mixer panel is an additive mixer.

author: BrianHG
author_rank: Super Contributor
timestamp: August 24, 2025, 01:59:41 pm
content: Anyone try out the free 3 day trial of:https://www.brain.fm/They say they do not use binaural beats, yet listening to their 'study' / 'focus', they are applying what appears to be a global volume modulation effect with added background noise. I'm not sure how they got so many positive reviews, with BS FMRI scans which only show a brain being globally over activated/stressed instead of proper focus in key regions dedicated to deep concentration. All I get is a headache from using it.Maybe if they focused on the quality of the artificial music instead of the BS effects, I might have considered it useful.I stick with real music.

author: paulca
author_rank: Super Contributor
timestamp: September 07, 2025, 11:30:36 am
content: How does this relate to the time domain, as in the delay component and reflections between ears and lobes.There has been some success in producing 3D spacial "feeling" from just 2 speakers. So this is tapping the brains millisecond delay perception and pattern matching of ear lobe reflections etc. Used to position sounds in 3D space in the world model.If you combine the two close frequencies in two ears could trigger a spacial sensation of the sound moving around.I believe it matters greatly what the waveform is too. IIRC a sine wave is very difficult for the ear to locate, forcing nearly everyone to "cock their head like a dog" when you play one. The impulse is to rotate your head to probably non-random angles to try and interrupt the phase and get a bearing on the signal.

author: RJSV
author_rank: Super Contributor
timestamp: September 23, 2025, 07:56:40 pm
content: One contribution to the discussion:When a single ear hears a sound, there is a crude sort of directionality due to the frequency response of the ear shape. I guess the brain has a highly complex response, that figures out direction.Example: A noise up and behind the head maybe has a certain brain response, with 'muffled' quality on the very high frequencies, or harmonics. Same noise more towards the front, or face, forehead etc. might be less muffled.So a cat or whatever, can track the nearby mouse, via this effect. But I'm not able to muse about how a brain gets the 'original template' or learns the original noise and expected harmonics. (Maybe researcher's don't yet know ?).But, for sure, that cat 'knows' roughly where the mouse is, using only one ear, and the response variations versus angle of reception.Plugging THAT in, I wonder how things work when a cat, or human has normal TWO ears working the mouse sounds, each with a decision about 'where', at what angle, into each ear.If each ear can find out the angle of arrival, then triangulation could give a crude estimate of both direction and distance for predator and prey interactions.Most CATS seem wired for Compulsive response, by focus focus focus, (when a higher frequency mouse sound is present nearby)!

author: RJSV
author_rank: Super Contributor
timestamp: September 23, 2025, 08:04:25 pm
content: One idea just now, is that, with a single ear, a MOVING source provides a sound that has a variation in perception. If the sound's high frequencies increase, then the brain can assume a source of that is currently moving towards the front of the head.That way, the animal doesn't need a big library of response types, just a relative sense, of frequency responses, now, and 100 msec. ago.(No matter how nominal the animal). (Hello, my friend)

author: RJSV
author_rank: Super Contributor
timestamp: September 24, 2025, 07:21:50 am
content: To member Temperance:I hesitated to bring up some hassles that cooled down, regarding aNALOG kID. But, he had been civil, but after s similar spate of uncool encounters (quick to issue the "Fuck You" to a non-familiar member).(I think I did read ONE Original Posted thread, since 2025 started.)I was annoyed, and then it got worse; He (a.k.) very consistently came back in (my) face, like 17 minutes after my post, and fired off some really just cheap, jerky, 'snark' I termed it: (approximate quotes):"Rick, that used record player you claim to be enjoying...is total garbage consumer product!". Ah-ha; now I know...uh...something ?"WE don't like reading your messed up Word Salad posts"Ah-ha! (Our self-appointed LEADER). Other members have expressed dismay, over the clarity of my posts, and it looks like he just picked up, on that. No value really.Thing is: he generally seemed to come back, hard, with some cheap, useless REPLY, and within less than 29 minutes after my own post.So it got to be an auto-learned near-phobia:"Ahhhh shittttt; There he is...only 17 minutes after my post, with a really stupid non-contribution!"Confronted, he issued the 'Fuck You then' reply...again after 12.5 minutes. I responded that:"Can you please,PLEASE wait an hour or something, before I get the thumbs down, from our newly self-appointed leader-boy ? !"But nope: even that got the snarky return, fuck you content-free utterance. He seems smart, like an A.I.Bot, he seems fast, like an A.I. bot might. Certainly no respect for Dave, and the real rules, for posts, like an AI. BOT.Recently, another member asked him to stop with the negativity, if he had nothing to contribute. (I felt my position get vindicated, by another reaction). But, he got better, on my topics at least, (so I laid off the defensive watching out, for his crap).Now, I read this, recent waste and chain-pulling of random member's topic discussion. Motivation psychology mentions:'Sadistic blah blah blah - narcissistic etc.'. was the jargon used, which I couldn't decipher, totally, (the motivation of disrupters).Smart, smarmy quick Disrupter. Has its basis, for the worthless antagonism...(in a bar maybe).Rick B.