B How does output voltage of an electric guitar work?

[Xenon02]

Sometimes it may clip, others not.

The peaks must sum at some point so it is rather when ?

Concerning what I put in italics: Get over yourself. It's a shame that things aren't the way I think they should be or would be, and everyone should accept that things are way I say they are, etc. Get over it and learn to accept that nature works the way it does and not how you think it should.

Ehhhhh, I am not saying that what I say must be the law ... I should really be careful what I say even if it's in jokes ?
What I tried to think all the time is if the peaks must sum at some point why didn't it happen in the website example ... was it to short to notice that peak sum ? Or is it rather random but it must happen ?

I see I accept what it is but I also ask why. I accepted your last post that they add up, the sum can be big so that it can distort etc. The signals aren't big as I imagined okey although with no proof as so I (I only used the example values from website or asked why it can't go bigger).

The values of both signals at any one time will add to produce a resultant. As one set of peaks runs through the other set of peaks, there will be instants when the two peaks add together. The rest of the time they do not coincide so the resultant will be less than 'cracking level'. The subjective effect will be the result over time of the signal addition.

Ok got it. Understood the phrase.

1. So in the examples it was just that the time was to short to notice these two peaks add up ?
2. What limits the vibration so the pickup doesn't produce big voltages from single string ? Or what are the values of the input in units.

 

[Averagesupernova]

The peaks must sum at some point so it is rather when ?

How should I know? It depends on the signals which are undefined at this point. I said sometimes they clip and sometimes not. Yes they sum. When the peaks all line up, they may not clip due to not enough signal level.

 

[Xenon02]

How should I know? It depends on the signals which are undefined at this point. I said sometimes they clip and sometimes not. Yes they sum. When the peaks all line up, they may not clip due to not enough signal level.

A okey, so this is what you meant.
And the one from the website didn't add up because there wasn't enough of time for this to happen on the oscilloscope ?

 

[sophiecentaur]

And the one from the website didn't add up because there wasn't enough of time for this to happen on the oscilloscope ?

Rather than taking some waveforms from a website, why not draw two waveforms with random peaks on them (neatly) on two strips of paper and see what the sums look like for different timing differences (phases). Sometimes the peaks coincide a lot and produce a high resultant sometimes hardly at all.

Thing is that with actual music from a musical instrument you can get all sorts of results. It will depends on the actual tuning of strings and instruments. Also the chords used in the music. In the end, it's often down to personal preference whether you perceive the sound as nice or distorted for the same amplifier. People (hifi buffs) are very fussy, often objecting to 'quality' with no just cause.

 

[Xenon02]

Rather than taking some waveforms from a website, why not draw two waveforms with random peaks on them (neatly) on two strips of paper and see what the sums look like for different timing differences (phases). Sometimes the peaks coincide a lot and produce a high resultant sometimes hardly at all.

I did something like this, one with 2 sinuses and one with 2 different shape signals. Here is the one with different shapes (g_1, h_1), it is hard to find that the sum is equal 6 : https://www.geogebra.org/graphing/merap3ws
I believe that the peaks of two not sinusoidal signals adds up at some point but this point is pretty hard to find (was doing it by hand by sliding the function all the time right ...).
I mean there is no reason for it that two peaks won't meet at some point. But I think you've tried to tell me that this sum might happen or not during the play.

Also it is not a real waveform I know it looks more like this I guess :

But didn't know how to approach making something like this ;D

But did I answer correctly ? is it that peaks add up but when it's unknown and it might not even happen during the play. Like in my example the peaks of g_1 and h_1 is y = 3, and the sum of those peaks is y = 6. I couldn't find it but it must have happened at some point but dunno when and during the play this might be neglected. So that's maybe why peak was 300mV and not 500mV because maybe 500mV could have happened but it was not enough of time or something like that or randomly one time can happen.

This is my interpretation of what I have drawn + your text.

 

[Averagesupernova]

I believe I've stated this before but open a spreadsheet program and plot some lines based on a repeating sine table. Step through at different rates to get different frequencies. Add some of these together and plot. Don't be afraid to experiment with this. It's not like your going send something into clipping and blow the computer up.

 

[Xenon02]

I believe I've stated this before but open a spreadsheet program and plot some lines based on a repeating sine table. Step through at different rates to get different frequencies. Add some of these together and plot. Don't be afraid to experiment with this. It's not like your going send something into clipping and blow the computer up.

I am not afraid it is that I have to write by hand every point of specific sine wave and I don't know if it's accurate and then find the peak of their sum.
The one I've sent already added 6 different sine waves, each 3 creating a signal not similar to sinewave and then again added, each can be shifted using the slider. The thing is that it's hard to find the max value.

That's why using previous experiments which was adding 2/3/4 sinewaves and shifting them the result was similar which was at some point the peaks added up (they had different frequencies).
So probably the E1 and E2 could add up but that time didn't come up. Same went with my example with 6 sinewaves where they have created random signal. And the peak Y = 6, didn't appear after checking x = 0 -> x = 5000, so perhaps it is somewhere.

So I deduced that maybe in the website the E1 and E2 their peaks didn't add up because there wasn't enough " time" for it to happen it was cut before it could happen, or randomly it could happen, changed the phase itp.

But also another thought came up chord was not only E1 + E2 but all 6 strings so tbh it's unknown what the peak could look like ;> Also maybe the frequencies of my signals where wrong in my last post example so that's why the smaller peaks was big Y = 5, and the real signals are slower (small frequencies).

TL:TR

- My previous example the signals where probably to fast compared to the real signals, that why 6 sinewaves had repeatable peak Y = 5 but couldn't find Y = 6 although it must have happened.
- This deduction Y = 6 must have happened at some point because signals with different frequencies there is a point where their peak adds up, proof first post.
- Chord from website is 300mV while E1 is 200mV and E2 is 300mV, maybe there was not enough time or a change for it to happen, because I scrolled through my example and didn't find Y = 6 after X=0 -> X = 5000 by hand it happened but dunno when
- Chord consist of more than E1 and E2 it's like using 6 strings at once, while one string of E1 is 200mV and E2 = 300mV dunno what is with the rest like E3 ... E6, so maybe frequencies are really slow that the peak was 300mV

 

[sophiecentaur]

But didn't know how to approach making something like this ;D

I am not afraid it is that I have to write by hand every point of specific sine wave

There is no need to plot an exact sine wave - in fact we have all said that real signals are not sine waves. The easiest shape to learn from would have a number of easily identifiable peaks amongst some lower levels.
Neither do you need to plot fuzzy signals waves like the real version. you posted. You just need to sketch (freehand) two similar signals without all that confusing fuzz (several cycles of the idealised shape I posted with different repeat rates).
I assume that you have looked at videos of typical guitar waveforms. Google can help you there.

I can't think why you want to consider six string chords before you have an idea of how two string chords work. Just get the basics first.

 

[Xenon02]

I assume that you have looked at videos of typical guitar waveforms. Google can help you there.

Found these images. Huh so they are repeatable signals,
Mine was also repeatable :

This is one string

This is second strong signal it repeats.
https://www.geogebra.org/graphing/merap3ws

So adding up will result in chaotic one. So the peak I saw most of the time were Y = 5.3, couldn't find Y = 6, it must have happened at some point but I couldn't find it.

But going into hand made like the one in the picture I will try to make it in paint if it's not a problem :

Changing the phase will make that peak of blue and read will match and appear as the Y = 100+200 = 300
I can change the phase of blue one so that it will match with the red peak value.
But even without changing the phase the peak will appear, somewhere ? Is it incorrect ?
I've recreated the effect in website and tried to explain what happens while shifting the blue or red signals. The website was easier to recreate but is also non-sinewave, it repeats at some point. So what is incorrect in the website version ? The Excel will be similar but with hand written values. Adding up the signal will result in similar effect like the handwritten one or the website one.

PS. My diagram from website I made is like this :

Which leads to the question if my diagram is incorrect ? Is my deduction also incorrect ? Yes, then why ?
I deduced that because E1 and E2 didn't add up is because there was not enough time ? the signal is long and for it to happen it takes time, or my signal is way to slow.

It's hard to deduce it having arbitrary stuff that's true ... But it just gives question why it did not happen, phase shift can only make this point happen faster or not.

 

[sophiecentaur]

But it just gives question why it did not happen

You have to accept that it must be down to magic, poor choice of waveforms or inaccuracy in any calculations. It's just a matter of Maths so you cannot argue with results arrived at by a valid path. Why would you want to. It really is time to stop all this; it is getting you nowhere and is boring me to death.

 

[Xenon02]

You have to accept that it must be down to magic, poor choice of waveforms or inaccuracy in any calculations. It's just a matter of Maths so you cannot argue with results arrived at by a valid path. Why would you want to. It really is time to stop all this; it is getting you nowhere and is boring me to death.

You know what now I have found my fault here, phase shift indeed makes difference when it comes to adding. Because in my examples it happened that even if there was one full cycle the signal didn't reach it's peak (like sum of three sinuses which is 1+1+1 = 3 so here it was 2.8 ?). I thought that after one cycle the signals peaks must add up.
But ! Each cycle the values are different although the shapes are the same, so it implies that the peaks can meet up am I right ?

Two cycles are here so yea. Even though they look similar they have different values at top which is visible in the blue marked values, because they have different value.

Indeed my signals might not be correct aswell as you've said, don't know why their sum was always huge hmmmm : https://www.geogebra.org/graphing/merap3ws - it's laggy. But shifting the phase makes the top value reduce and the bottom increase.
So it is I think basic math but am I right that at some point the peaks add up after x-cycles ??

So I now know why adding E1 and E2 which are 300mV and 200mV might have not added up which was 500mV, although in my example they still where high, so the peak should have been like 350mV or something and it was only E1 and E2 but chord has E3 ... E6 hmmmm but I am getting to something I guess.

Okey just say if I am wrong or not. No matter the phases the peaks up will add after x-cycles at some point yes or no ?

Sorry for borring you here. I just saw something I just kept thinking was correct. But each cycle had different peak values so I rethinked it a bit.

 

[f95toli]

What do you mean by not tied together ? Chord consists of these two signals. So there were 2 signals separate and 2 signals together at the same time.

Not sure I want to get involved in this discussion; but it is perhaps worth pointing out that the bit in bold not correct. If you play a chord on an electric guitar you are still only getting ONE signal, simply because the output signal is still mono. The fact that the signal can be decomposed into different frequencies is irrelevant: in the time domain (which could be argued is the most "physical" domain) it still one signal; at any given time the amplitude has one single value.

it might be worth considering that you can use a microphone which (usually) has ONE membrane that vibrates can still be used to record a chord played on a guitar.

Also, remember also that the way we usually decompose signals into different frequencies is not unique, using sine and/or cosine is usually the simplest, but there are an infinite number of ways of decomposing a signal and the different ways will have a different number of components (wavelets would be a good example).
We have become so used to Fourier transforms that we sometimes forget that this is just a mathematical technique,albeit a very convenient one.

 

[Xenon02]

Not sure I want to get involved in this discussion; but it is perhaps worth pointing out that the bit in bold not correct. If you play a chord on an electric guitar you are still only getting ONE signal, simply because the output signal is still mono. The fact that the signal can be decomposed into different frequencies is irrelevant: in the time domain (which could be argued is the most "physical" domain) it still one signal; at any given time the amplitude has one single value.

Interesting, I thought that it consist of all sounds. Or to better say it, that one string makes E1 sound, string nr.2 makes E2 sound, so making E1 and E2 sound at the same time so both are theoretically added the most logical way because you hear both of these sounds + there are 2 vibrating strings and not one. The output which amp is taking the signal is of course single signal. It's rather of the input how it is added and the output result.

That's why I was starting experimenting with functions how do they look like, add up etc.

 

[sophiecentaur]

Not sure I want to get involved in this discussion;

I'd love for you to take over: I'm just exhausted.

 

[Xenon02]

I'd love for you to take over: I'm just exhausted.

Dang it ;)
I mean I thought I was getting to something ;D

 

[Averagesupernova]

You know what now I have found my fault here, phase shift indeed makes difference when it comes to adding.

I don't know how this discussion has gone on as long as it has without that realization. This would have revealed itself had you plotted some some waves out in a spreadsheet or on paper. Doing it on a spreadsheet is not that difficult. You don't have to manually enter values into each cell. Set up a group of cells that increment by a certain amount. Go from there. Copy and paste is your friend.

 

[Xenon02]

I don't know how this discussion has gone on as long as it has without that realization. This would have revealed itself had you plotted some some waves out in a spreadsheet or on paper. Doing it on a spreadsheet is not that difficult. You don't have to manually enter values into each cell. Set up a group of cells that increment by a certain amount. Go from there. Copy and paste is your friend.

I've made some arbitrary numbers to create a one cycle and copied it. After the plotting each cycle has similar shape but different value. Changing the phase changed the shape a bit. But there because each cycle had a bit different value but similar shape it

It's hard for me to deduce it ... Because when I was using sin(x + a), sin(pi/2 x + b) and sin(pi/3 x +c ) they very much changed the values drastically, and the tops overlaped less or more.

When I changed into sin(2pi x + a), sin(2pi *2x + b) and sin(2pi*3x+c) then the peaks were more constant ...

Here the green is pretty consistent, hence :

No matter how many cycles passed the peaks are the same and didn't reach value Y = 3. Which confuses me mathematically because I might be dumb here again.

I don't know now because faster signals should catch up to slower signals at some point so that peaks should match at some point and result in Y = 3 after x-cycles.

Now I don't know, does signals with different frequencies will always have that one point where their peaks add up ? In one example with sin(x + a), sin(pi/2 x + b) and sin(pi/3 x +c ) it showed that fast signals slowly catched up to slower signals so that peaks where bigger at times like in first picture, in the other example it showed that faster signals never catched up to slower ones so that peaks match up.

I am now confused mathematically, and can't deduce from making excel sheet nor with this graphical web. Whether the peaks of signals with different frequencies must add up no matter the frequencies (no matter means here that after x-cycles the peaks match, changing frequencies changed the time when this happens). If not I wonder now why when in one the fast one was catching up to slower one and the other it was all the time the same ......

Confusion lvl 100.

 

[Averagesupernova]

Start with the fundamental (lowest frequency). The higher frequencies should always be smaller than this. Also, until you understand some of this better, just use two signals total. Experiment with different frequencies that are not exact harmonics of the fundamental. You will get this if you play with the plots long enough.

 

[Xenon02]

Start with the fundamental (lowest frequency). The higher frequencies should always be smaller than this. Also, until you understand some of this better, just use two signals total. Experiment with different frequencies that are not exact harmonics of the fundamental. You will get this if you play with the plots long enough.

Yea just checked it.
Phase changes the max peak value. https://www.geogebra.org/calculator/myxxzexe - tested with 2,3,4 signals. Each added with shifted phase could reduce the max amplitude, was able to reduce it to 2 max amplitude (dunno if I can lower it having 4 signals maybe different frequecies ?). Changing the faze I can get bigger amplitude, but not max which was Y = 4 (to big steps of the phase shift maybe).

Well so phases changes the peak. But there is still a question.
What is the max amplitude value of one string ? Do strings have different max values of the amplitude ?

Also it is a phase shift so E1 and E2 if happened that the phase was shifted enough to add 300mV and 200mV and other signals peaks, then it will for sure ? Exceed 0.7V and it is periodic so the distortion will be heard :

So playing the same chord can bring this distortion but it was mentioned it would be not heard although distortion is hearable in rock music (it has that specific metalic/cracking sound). Which videos show how it sound with and without distortion.

So yea it is probability that the phase will align so that all peaks are added (like E1 300mV and E2 200mV and other that are not mentioned). It is a chance.

If this question even have sens, then distortion happening when the luck will happen playing the same chord and add all peaks. That it will not distort. Playing the same sound over and over and distortion happens. And it will be hearable. So I wondered what is the max single string amplitude value, or does every single string on the guitar has it's own max amplitude value which cannot exceed.

 

[Averagesupernova]

Ok, you mentioned alot in the last post but I'm only going to address one thing for now. Rethink/experiment after you read what I have to say.
-
Changing phase will NOT change the peak amplitude. The peak amplitude will occur every so many cycles repeatedly. Changing frequency will change how often this peak occurs. Pretty basic stuff from a signals and systems standpoint.

 

[Xenon02]

Changing phase will NOT change the peak amplitude. The peak amplitude will occur every so many cycles repeatedly. Changing frequency will change how often this peak occurs. Pretty basic stuff from a signals and systems standpoint.

Hmmm
So my example here

Should at one point have Y=4 ? It was most of the time Y=2.09 or a little bit bigger like Y=2.1 and not higher after looking at many cycles.

Same signal but different phase of one of 4 signals, and top value is 3.14. Max sum can be 4 because 4 signals with amplitude 1. But here it was constantly 3.14, sometimes 3.12 or 3.15 but not heigher. But I only changed the phase and the sum changed.

Hmmm I'll check somethings. Because if it not changes the peak.
But when I changed the phase the top value changes so hmmm but how often it occured was less often.

 

[f95toli]

Interesting, I thought that it consist of all sounds. Or to better say it, that one string makes E1 sound, string nr.2 makes E2 sound, so making E1 and E2 sound at the same time so both are theoretically added the most logical way because you hear both of these sounds + there are 2 vibrating strings and not one. The output which amp is taking the signal is of course single signal. It's rather of the input how it is added and the output result.

That's why I was starting experimenting with functions how do they look like, add up etc.

No, the strings vibrate inside the magnetic field from the pickup; this generates a signal out but there is onLy ONE signal coming from the pickup (the situation is obviously a bit different for an acoustic signal).
Try looking at a sample of a someone playing chord on an electric guitar; at any given time the amplitude has ONE value. The fact that the signal can be decomposed into many frequencies does not change that.

 

[Xenon02]

No, the strings vibrate inside the magnetic field from the pickup; this generates a signal out but there is onLy ONE signal coming from the pickup (the situation is obviously a bit different for an acoustic signal).
Try looking at a sample of a someone playing chord on an electric guitar; at any given time the amplitude has ONE value. The fact that the signal can be decomposed into many frequencies does not change that.

I am confused, the pictures I've shown are one signal in fact. The sum is just each sound that are decomposed from the output.
Okey so E1 has a specific output, E2 also a specific output, playing E1 and E2 at the same time will produce a different single output but decomposing it will consist of E1 output and E2 output but added. It is a single output like you've said it just consist of E1 and E2 because you hear them.

Nevermind for now I'll now focus on what Averagesupernova said, because it is still superposition, the chord consist of each string sound so it can produce the output which is a single signal. And I have a feeling of lack of understanding the additive part of each signals.

I'm slowly getting it and soon will close the subject and move on. Because I can see that it can be repetetive. But I am confused of what is different to what I have shown in pictures. It is one signal.

 

[Xenon02]

Idk

I think I'll just stand with this version :

Changing the phase of signals will change the amplitude of the sum of all signals. Like here one signal was being changed (it's phase), and the amplitude of the sum changed. So the peak value of periodic signal here can change and doesn't have to be the sum of all peak signals separately. Phase matters etc.

 

[Averagesupernova]

Show us a plot with the fundamental frequency and a single non-integer harmonic that is about a quarter or less of the peak to peak value of the fundamental. Take enough cycles you will find that the cycles eventually line up. Your peak just moves farther out. You are not waiting for enough cycles to go by in your case.
-
If you just use the fundamental and a very close frequency you will see changes. But you have wait longer for more cycles and the peak will show up. Try adding two signals of the same frequency and yes, phase matters and you will never see any peak different than the previous. Also, keep in mind that X degrees of phase change on the higher frequency signal doesn't move those peaks very far between the peaks of the lower frequency signal.

 

[Xenon02]

Show us a plot with the fundamental frequency and a single non-integer harmonic that is about a quarter or less of the peak to peak value of the fundamental. Take enough cycles you will find that the cycles eventually line up. Your peak just moves farther out. You are not waiting for enough cycles to go by in your case.
-
If you just use the fundamental and a very close frequency you will see changes. But you have wait longer for more cycles and the peak will show up. Try adding two signals of the same frequency and yes, phase matters and you will never see any peak different than the previous. Also, keep in mind that X degrees of phase change on the higher frequency signal doesn't move those peaks very far between the peaks of the lower frequency signal.

I took it that the first frequency is 2Hz while the second one is 3Hz do the second one is as I read non-integer.
After like X = 630, didn't count the exact cycles their sum didn't change much.

Top value wasn't changing alot.

Values I've noted :
Y = 1.1598118242943, X = 3
Y = 1.1598118242939, X = 100
Y = 1.1598118242940, X = 224
Y = 1.1598118242938, X = 352
Y = 1.1598118235486, X = 724
Y = 1.1598118236484, X = 1251
Y = 1.1598118197268, X = 1430
Y = 1.1598118170228, X = 1509
Y = 1.1598118205792, X = 2139
Y = 1.1598118197515, X = 2784
Y = 1.1598118242948, X = 3123

It was dropping to 81 then again back to raising to 82. I can imagine that faster signal can catch up to slower but here it is a bit random. Like I could never reach that moment because it is not constantly raising. At some point it was going back to square one. Here till 1509 it was decreasing and from that it was raising at 2139 and again from there it was decreasing and again back to increasing.

It was decreasing, and at some point it was again increasing but didn't find the moment though.
For the same frequency I can imagine that their peaks won't add up if their frequency is not matched.

 

[Tom.G]

Try when the 2 signals are relatively prime to each other in frequency -- perhaps 3 Hertz and 7 Hertz.

If you plot enough cycles of the output, you should see a result where the amplitude repeats every 21 cycles of the output.

Cheers,
Tom

 

[Xenon02]

Try when the 2 signals are relatively prime to each other in frequency -- perhaps 3 Hertz and 7 Hertz.

If you plot enough cycles of the output, you should see a result where the amplitude repeats every 21 cycles of the output.

Cheers,
Tom

Indeed in 3Hz and 7Hz amplitude repeats itself.

But I think Averagesupernova

Changing phase will NOT change the peak amplitude. The peak amplitude will occur every so many cycles repeatedly. Changing frequency will change how often this peak occurs. Pretty basic stuff from a signals and systems standpoint.

So I interpreted it that changing the phase will not change that the max amplitude will be when two signals will be in phase at one point. In other words peaks of each signals at some point should add up. Because peak will no change.
So I went with this idea but I see it is repeating the amplitude which was : 1.1998263829145 for 3Hz and 7Hz each 21 cycles. So I dunno when Y = 1.25 which is max because changing phase doesn't change the peak as it was said. Or I misunderstood it.

 

[Xenon02]

If you just use the fundamental and a very close frequency you will see changes. But you have wait longer for more cycles and the peak will show up. Try adding two signals of the same frequency and yes, phase matters and you will never see any peak different than the previous. Also, keep in mind that X degrees of phase change on the higher frequency signal doesn't move those peaks very far between the peaks of the lower frequency signal.

So I've given two signals and they weren't getting any bigger infact it was repeating at some point. The peak didn't get to the max which is Y = 1.25 and changing phase shouldn't change that the Max peak should occur.

 

[berkeman]

So I've given two signals and they weren't getting any bigger infact it was repeating at some point. The peak didn't get to the max which is Y = 1.25 and changing phase shouldn't change that the Max peak should occur.

I haven't been following this thread for a while now, but can you say a bit about your background so far in Signals & Systems? Have you taken any classes in how signals work, or found any good technical articles? What is your background so far in trigonometric functions and the math involved with them?