Talk:Beat (acoustics)

message: Can someone verify, if the example is legit? For all other sounds I heard the pulse, when listening with both earphones and stopped hearing the pulse, when listening with only one earphone. But for the "220/222 Hz example" I always hear the pulse, no matter what earphone I use.  — Preceding unsigned comment added by 2003:FB:F1B:3BE3:115D:BEF5:D683:B387 (talk) 08:07, 26 June 2023 (UTC)
thread_title:  Beating waveforms (low frequency) example (220/222 Hz)

message: I just changed the identity to read 4a on the right. This is correct isn't it? Also, why the amplitude in terms of 2a in the first place? Couldn't it be simplified to read just a? -- postglock 15:52, 16 August 2005 (UTC)
replies: text: In origin the amplitudes were indeed a, but I got mistaken when converting the identity to TeX. Gonna fix that.--Army1987 22:18, 16 August 2005 (UTC)
thread_title:  Identity 

message: I find the justifying equation quite daunting until you realize that, for the sake of simplicity, most constants can be ignored. In addition, a variable change gets rid of the two fractions and make things clearer.
This is what I propose:
:Let's consider the sum of a first sound S_1 of requency f_1 and a second sound S_2 of frequency f_2. The expression of these sounds are:
:\begin{align}\\
S_1 &= \sin(2\pi f_1t)\\
S_2 &= \sin(2\pi f_2t) \end{align}
:We define two variables a and b that represent the median and the half-difference of the two frequencies:
:\begin{align}\\
a &= 2\pi\frac{f_1+f_2}{2}t\\
b &= 2\pi\frac{f_1-f_2}{2}t \end{align}
:Using angle sum and difference identities, we can deduce
:\begin{align} S_1+S_2 = \sin(a+b)+\sin(a-b) = 2\sin(a)\cos(b) \end{align} 
Well, I think this reads better than the original:
{ a\sin(2\pi f_1t)+a\sin(2\pi f_2t) } = { 2a\cos\left(2\pi\frac{f_1-f_2}{2}t\right)\sin\left(2\pi\frac{f_1+f_2}{2}t\right) }
We could also make the transformation explicit:
\begin{align}
\sin(a+b)+\sin(a-b) &= \begin{align}\sin(a)\cos(b)&+\cos(a)\sin(b)\\
+\sin(a)\cos(b)&-\cos(a)\sin(b)\end{align}\\
&= 2\sin(a)\cos(b) \end{align}
(Here, the "+" should be indetend further than the two "=", while retaining proper alignment of the two upper terms, but I don't know how to do that) Exxos77 21:40, 25 May 2007 (UTC)
thread_title:  Making the equation more readable 

message: For an example in music, popular American punk band At the Drive-in have a song called "pickpocket" which uses notes a step apart to create beating. It's most prominent in the introduction of the song. 129.11.122.215 14:04, 22 September 2007 (UTC)
thread_title:  Example in music 

message: It is said: "This is caused by slight differences between the intervals of equal temperament and the "natural" intervals of the harmonic series". While this is, strictly speaking, possible, that's not what I had in mind when I originally wrote that sentence back in... (Who cares when?). I was thinking about out-of-tune notes.
In the specific example of a fifth, using for example C4 and G4, the third harmonic of the former is 784.88 Hz and the second harmonic of the latter is 783.99 Hz. They beat at less than 1 hertz, and most times notes are played for much shorter than 1 second.
Also, the interval between a just-intonation fifth and an equal-temperament fifth is less than two cents, while the just noticeable difference for the human ear is 5 cents, so it means that in practice often instrument aren't tuned to such accuracy.
On the other hand, should the G4 be 15 cents too sharp, its second harmonic would be 790.81 Hz, beating at almost 6 Hz and immediately noticeable.
So the inexactness of ET, if mentioned, should be introduced as a possible cause of beating (e.g. "This can also be caused"...), and a "worse" interval (e.g. the  ET major third at −14 cents from the exact one) should be used for the example.
Army1987 (talk) 11:06, 15 June 2008 (UTC)
replies: text: The effect happens in both out-of-tune notes and ET notes. You are welcome to phrase it however you like, but I think ET should be mentioned as a cause for beats as well. Barak Sh (talk) 18:21, 15 June 2008 (UTC)
thread_title:  Beating near to harmonic intervals 

message: This material appears in many undergraduate physics texts. Just for grins, how about citing a couple...? Rb88guy (talk) 19:07, 4 September 2009 (UTC)
thread_title:  No references 

message: (moved from User talk:Oli Filth)
You deleted my bit on doppler-shift ultrasound in the beats section, saying that it was probably irrelevant.  It's not! Beats is exactly what is used to observe and measure the small frequency shift between reference signals and those reflected.  Do you want to argue this further?  I'd be happy to...  —Preceding unsigned comment added by Bhindibhagee (talk • contribs) 14:54, 20 April 2010 (UTC)
replies: text: I didn't say it was "irrelevant".  I said that this is almost certainly reliant on a heterodyning operation, which is similar, but subtly different.  I don't have any sources to back this up, but this sounds like a standard mix-down operation to me.  Oli Filth(talk|contribs) 15:30, 20 April 2010 (UTC)
thread_title:  Ultrasound edit 

message: There was a section on "difference tones" that contained the following unsourced content:
"If the beating frequency rises to the point that the envelope becomes audible (usually, much more than 20 Hz), it is called a difference tone.[citation needed] The violinist Giuseppe Tartini was the first to describe it, dubbing it il Terzo Suono (Italian for "the third sound"). Playing pure harmonies (i.e., a frequency pair of a simple proportional relation, like 4/5 or 5/6, as in just intonation major and minor third respectively) on the two upper strings of a violin, such as the C above middle C against an open E-string, will produce a clearly audible C two octaves lower. An interesting listening experiment (help·info) is to start from a perfect unison and then very slowly and regularly increase the pitch of one tone. When one tone starts to split out from the former twin-note, a slow rumbling can be heard, gradually increasing into an audible tone."
This is completely incorrect. An obvious counterexample would be to take a 100 Hz sine wave sin(100*2pi*t) and modulate it by another 100 Hz sine wave sin(100*2pi*t). Since the envelope is 100 Hz, by this (completely unsourced) theory, we should hear a 100 Hz audible tone in the result. Obviously, we don't; a 100 Hz tone is present neither mathematically nor audibly via naive experiment. sin(100*2pi*t)^2 = 1/2 - 1/2*cos(200*2pi*t), so what we end up getting is a 200 Hz tone with some DC offset.
Given a signal s(t) and an envelope e(t), it's a very, very common but *completely wrong* misconception that the spectral content of the envelope is present in the combined signal s(t)*e(t), which leads to the further misconception that if e(t) becomes fast enough to "be audible," you'll hear it. This is only true if s(t) has a nonzero frequency response at DC, and is false otherwise. You can see some computed AM spectra at , which clearly shows that the spectral content of the modulator isn't present in the mixed signal.
Another reason that the "envelope" might "become audible" is if some nonlinear system is present which is actually creating intermodulation distortion, e.g. literal sum and difference tones. This is a *completely* different phenomenon from beating and should never be confused with it.
I've deleted this entire section; I don't know how to salvage it.
Battaglia01 (talk) 01:27, 3 April 2013 (UTC)
replies: text: I seem to recall Feynman mentioning something about difference tones due to the human hearing being non-linear.  I might look at that when I have some spare time.  — A. di M.  08:46, 5 April 2013 (UTC)
replies: text: Correct, it is - or, if your speakers are nonlinear, or the microphone you used to record something is nonlinear, or if the instrument you're playing on exhibits nonlinear effects, all of which happen decently often. Feynman is probably talking about DPOAE's. But, generally speaking, true "combination tones" (not necessarily the simple quadratic difference tone) actually appear if the signal is being sent through a nonlinear system of some sort, which means that they have nothing to do with "beating" at all and they certainly don't have to do with "beating becoming audible." The only discussion about "difference tones" that should appear on this page is one about how it's NOT related to beating. Battaglia01 (talk) 20:08, 6 April 2013 (UTC)

text: User Battaglia is describing what happens when two sines of different frequency are _multiplied_ together ("modulation"). However, this article discusses two sines _added_ together. So Battaglia's reasons for discrediting the removed text are invalid. I haven't dug up the full removed text to determine what it was trying to say, but the section quoted here seems plausible. Meanwhile, the discussion above of nonlinearity (due to acoustic environment or hearing) means that even though the article discusses addition of two sines of different frequencies, the result is not just the linear sum of amplitudes, but also results in some amount of signal at frequency components similar to those produced by multiplying. That's of some interest, but doesn't bear on the removed text. Gwideman (talk) 15:12, 19 August 2017 (UTC)
thread_title:  Difference Tones - unsourced and completely wrong! 

message: In one of the samples, it is written that frequencies 300 and 310 produce a beat frequency of 12.35 Hz. This is obviously not correct. It goes on to say that 300 Hz is the A3 tone and that 310 is the G#3 tone. These frequencies are not correct. And furthermore, why would G# be *higher* than A3? The description of this sample is incorrect in so many ways. I'm going to remove the description entirely, but I will leave the sample in case anyone cares to figure out which two frequencies are really beating against each other.  — Preceding unsigned comment added by 198.182.13.47 (talk) 14:37, 30 October 2015 (UTC)
replies: text: You're right, those frequencies made no sense at all. I've put them back to how they were in April. Burninthruthesky (talk) 15:24, 30 October 2015 (UTC)
thread_title:  Sample: the description is wrong. 

message: This image from another article:
could be used or adapted for use in this article. 71.166.96.62 (talk) 19:07, 26 November 2015 (UTC)
thread_title:  Suggest using animation from another page 

message: Substituted at 09:17, 29 April 2016 (UTC)
thread_title: Assessment comment

message: I think the picture at the top is misleading. (https://upload.wikimedia.org/wikipedia/commons/2/2e/Beating_Frequency.svg).  It looks like there are 2 signals multiplied together, not added as happens with beats.  Also, the values used in the formulas don't give a clear picture of how the beating frequency is calculated.  Am I missing something or should this picture be changed?  — Preceding unsigned comment added by 2602:306:B8BC:3300:11A9:F1AE:4DF3:6D36 (talk) 22:55, 23 October 2017 (UTC)
thread_title:  Top Picture 

message: The idea that the beat takes place between the two ears needs references.
I could be that just the amplitude increasing and decreasing could entrain brain waves - but only this paper shows that the two ears are needed  :
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2741401/
more links:
http://www.stealthskater.com/Documents/Lucid_07.pdf
<redacted>
The next link is a key source of the phenomena:
<redacted>  — Preceding unsigned comment added by 108.243.106.82 (talk) 15:16, 19 December 2017 (UTC)
replies: text: I removed the links to the Lane ref () and the Oster ref () as they violate WP:COPYLINK.  Otherwise, I am not sure what you are asking. Jytdog (talk) 18:16, 19 December 2017 (UTC)
thread_title:  Evidence lacking 

message: Can someone check the validity of the explanations given in the binaural beats section? The example in the text and the two sound files imply that the slightly discordant tones produce the illusion of hearing a third tone of 10 Hz or 3 Hz or 2 Hz. But the lower threshold of human hearing is 20 Hz, so an illusion of hearing those lower frequencies would be the illusion of hearing nothing, no? Largoplazo (talk) 02:01, 26 January 2018 (UTC)
thread_title:  Perceiving the unperceivable frequency