How does output voltage of an electric guitar work?

[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.
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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.
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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?

 

[Xenon02]

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?

I've had some classes about Signals & Systems but I wasn't very great at them. I knew how to use transformation from time to frequency domain and vice versa. I've been introduced into stuff like white noise. There where probably other stuff that I do not remember because I couldn't understand why it was used that way. So I only learned how to use patterns.

Trigonometric functions it depends. I know basics also from classes, I don't know if Fourier is one of them. That complicated function can be reconstructed using sin() and cos() functions. I don't know what I can say more tbh.

I've tried to plot some functions and from one side it should add up and from the other it should repeat so if it repeats then it won't reach peak. Or that the signals don't add up that output is one signal, I know this one but reconstructed from sin() and cos() and they consist of these used sounds that can be separately also played. So adding separate signal should give similar result as the already summed signal (which is single) if they have the same faze.

So I've made these plots and waiting for approval or disapproval.

 

[Averagesupernova]

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.

Ok based on what you say here I believe that your results confirm my prediction? Or am I misunderstanding?
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There are a lot ways to understand what happens when adding sine wave of different frequencies. If you have access to some LEGO blocks or something of this nature take a series of blocks of one size and lay them end to end. Do the same thing with a different size. Notice where the blocks join in each row and how the joints sometimes line up and sometimes don't. No matter how you do it by shifting the rows the space between where the joints line up will always be the same distance.

 

[Xenon02]

Ok based on what you say here I believe that your results confirm my prediction? Or am I misunderstanding?

Well this is 3Hz and 7Hz with basic phase dang = 0

There it was Y = 1.25

And shifting one signal the faster one :

It was max 1.19, so changing phase changed the max peak ... And this one never reaches 1.25 because it repeats the same values after 21 cycles. So in fact changing phase can lead to the point where peaks of individual signals won't meet and add up. Similar to the signals with the same frequency.

 

[f95toli]

I've had some classes about Signals & Systems but I wasn't very great at them. I knew how to use transformation from time to frequency domain and vice versa. I've been introduced into stuff like white noise. There where probably other stuff that I do not remember because I couldn't understand why it was used that way. So I only learned how to use patterns.

I am now a bit confused. If you were taught how to do a Fourier transform to- and from the time domain, that should have already answered your question, right? Because it is fairly clear that your question is not about guitars but how signals are represented in the two domains

 

[Xenon02]

I am now a bit confused. If you were taught how to do a Fourier transform to- and from the time domain, that should have already answered your question, right? Because it is fairly clear that your question is not about guitars but how signals are represented in the two domains

I also mentioned that I've learned how to use patterns or rather answer a question at that time, I didn't understand truly why I had to change one domain to another.
My question was about adding signals and why it was not equal to the one in the website from first post. So I was following what Averagesupernova and Tom.G said and made these plots.

What I understood from Averagesupernova is that signals with different frequencies no matter the phase will always have the peak value equal to the sum the signals peaks. For example Signal 1 = 1 and Signal 2 = 0.5, no matter the phase their peak is equal always Y = 1.5. And that the phase will not change the peak value. In my case I changed the phase and it was not Y = 1.25 which is max it was smaller. But maybe I misunderstood this part.

Tom.G told me that it was easier to see combining 3Hz and 7Hz that it repeats every 21 cycles. So infact this gives me the answer that after 21 cycles if it repeats and didn't reach Y = 1.25 then it will never reach this value, so phase changed something. If I had a phase that Y = 1.25 instead of Y = 1.09 then I changed the peak value.

You've mentioned that the output is one signal. Okey I understand this and the final results I always show as 1 signal output. But it consists of 2 signals because you hear them so it must consist these 2 signals in that one signal (the sum of 2 gives 1 output signal).
So I wondered if the phase mattered and that is why E1 = 300mV and E2 = 200mV gave a result of Chord= 300mV which was weird at first. Second of all Chord consist of 3 up to 6 strings sound so there are more like D = 200mV or something But it somehow Chord was 300mV just as if only E1 was played. But here comes the phase maybe that is the answer but I saw some conflicts that phase doesn't change it etc.

So that's why I am plotting more functions and show what is not crystal clear to me.

 

[Averagesupernova]

Aren't we starting to nitpick here about how close to peak is actually peak? 1.19 is within 5% of 1.25. The more cycles that exist between peaks the less ripple there is in the peaks as phase is shifted. This would represent a situation of using say 1 Hz and 1.01 Hz. Naturally you will be waiting a while for the peak to come along. Conversely, if you have signals of 1 Hz and 100 Hz you have many cycles of 100 Hz riding on top of the 1 Hz signal. It would be difficult to say that the peaks change very much as phase shifts. How far do you want to resolve top of the sine wave to in order to say that they change? There will be an area between those extremes where where some ripple in the peaks exists as phase is shifted.
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It seems you have done as I asked generating these plots with various signals. Keep it up. You've absorbed too much to quit now unless you are only interested in being right on a technicality. If that's the case I'll tell you the world is flat and walk away.

 

[Xenon02]

Aren't we starting to nitpick here about how close to peak is actually peak? 1.19 is within 5% of 1.25. The more cycles that exist between peaks the less ripple there is in the peaks as phase is shifted. This would represent a situation of using say 1 Hz and 1.01 Hz. Naturally you will be waiting a while for the peak to come along. Conversely, if you have signals of 1 Hz and 100 Hz you have many cycles of 100 Hz riding on top of the 1 Hz signal. It would be difficult to say that the peaks change very much as phase shifts. How far do you want to resolve top of the sine wave to in order to say that they change? There will be an area between those extremes where where some ripple in the peaks exists as phase is shifted.

Hmmm indeed comparing it to 3Hz and 32Hz signals, shifting doesn't change top value alot maybe like 1%.
With the 3Hz and 7Hz it was close as you've mentioned.

I was just thinking that phase shifting will never change the peak and if peak is 1.25 then it always must be like that. That's how I interpreted it when you've mentioned that phase doesn't affect the peak so I took it as a granted and took a better look at it.

I'm sorry if I was trying to nitpick it, I take things too literally and if it doesn't match what I see then I have questions ;>

Although for signals like 2Hz and 3Hz it was affecting more but I may understand why because like you've said if there are more cycles between peaks then the peak will be more accurate. So in other words if the second signal is much more faster than the first signal.
But I don't understand : "This would represent a situation of using say 1 Hz and 1.01 Hz.", the fast and slow signals show how often the peaks add up the signals that are so close to each other the phase matters I guess. I might have again misunderstood.

Overall I understood that :
- if we have 2 signals which the second signals is much faster than first then phase shift doesn't matter
- if we have 2 signals each are pretty slow then phase shift matters example 2Hz and 2.01 Hz :

- The more similar are both signals the more phase matters.

Hmmm so maybe that why adding 4 signals It looked like this :

It reduced alot it doesn't get to the peak which was Y = 4. Maybe because signals where to slow. I guess.

It seems you have done as I asked generating these plots with various signals. Keep it up. You've absorbed too much to quit now unless you are only interested in being right on a technicality. If that's the case I'll tell you the world is flat and walk away.

Don't worry I am not only interested in being right on technicality I just took it to literally. That's why I prefer to repeat what other said and give my interpretation to see if I understood it correctly. If not then I can read and try again.
Thanks again for the help as always :)

Oh but about flat earth, isn't it more of an concept of Truman show ? Which there is a huge blue globe and everything is just a show heh.

 

[Averagesupernova]

But I don't understand : "This would represent a situation of using say 1 Hz and 1.01 Hz.", the fast and slow signals show how often the peaks add up the signals that are so close to each other the phase matters I guess. I might have again misunderstood.

Overall I understood that :
- if we have 2 signals which the second signals is much faster than first then phase shift doesn't matter
- if we have 2 signals each are pretty slow then phase shift matters example 2Hz and 2.01 Hz :

Adding 1 Hz and 1.01 Hz (or 2 Hz and 2.01 Hz will result in a signal that takes 100 seconds to go from peak to the next peak. Again, I feel like you are making the mistake of not realizing that there are no limits on when you can expect the next peak. No one has defined that all the measurements need to be taken in a second or two.

 

[Xenon02]

Adding 1 Hz and 1.01 Hz (or 2 Hz and 2.01 Hz will result in a signal that takes 100 seconds to go from peak to the next peak. Again, I feel like you are making the mistake of not realizing that there are no limits on when you can expect the next peak. No one has defined that all the measurements need to be taken in a second or two.

A yea I didn't check to much then, I went through 1120 cycles and it was from 0.84 like in the picture to 1.249 which was close.
But from this description I should understand that any signal that doesn't have the same frequency will match at some point (with smaller difference like there 5%) ??

Even this signal :

It has 2Hz and 5Hz, it was usually 1.137 and I went pretty far but I understand at some point it will be 1.24.... or a bit smaller closer to the 1.25, maybe not exactly 1.25 but close.

Or even this signal :

Which was usually 2.1 but at some point it will be close to 3.8-3.9 ???

I expected some limits because at some point it just repeats like 3Hz and 7Hz in which after 21 cycles it repeated. So it had some time to add up and it repeats and there will be no more progression other than repeated ups and downs.

 

[pbuk]

So that's why I am plotting more functions and show what is not crystal clear to me.

As well as plotting more functions I think you need to take a step back and understand that the peak voltage of a waveform is almost completely irrelevant to what it sounds like. As I believe was stated dozens of posts ago, volume is determined by averaging over time (RMS).

You seem to have got lost in plotting graphs on a computer: this has nothing to do with anything you need to know about guitar pickups or signal processing (whether analog or digital). If that is what you want to learn about, follow the link @berkeman gave you in post #4.

 

[Xenon02]

As well as plotting more functions I think you need to take a step back and understand that the peak voltage of a waveform is almost completely irrelevant to what it sounds like. As I believe was stated dozens of posts ago, volume is determined by averaging over time (RMS).

You seem to have got lost in plotting graphs on a computer: this has nothing to do with anything you need to know about guitar pickups or signal processing (whether analog or digital). If that is what you want to learn about, follow the link @berkeman gave you in post #4.

I've read both links : https://nsinstruments.com/principles/linear.html , https://www.yamaha.com/en/musical_instrument_guide/electric_guitar/mechanism/mechanism002.html

In the first this catched me :
"We can, then, think about the combination of two waves of different frequencies as the combination of two waves of the same frequency with a continually changing phase relationship. The phase of the higher frequency wave will be advancing at a constant rate relative to the lower, and the phase of the lower frequency wave will be advancing at a constant rate relative to the higher."

"Since the phase difference between waves of different frequencies is constantly changing, the amplitude rises as the phases approach alignment, and then falls as the phases fall out of alignment, rising again as the waves approach alignment again."

The sound in the Anatomy of a Wave was said to measure using time domain, RMS in time domain or frequency.
I thought peaks are important because of how distortion is created :

If volume is about RMS, then ok. If the peaks are the same but RMS changed then something must have changed for sure. https://www.bbc.co.uk/bitesize/guides/zdc6fg8/revision/2 - I heard that amplitude, the bigger the louder in some classes.

With Averagesupernova I was trying to understand how the adding looks like because I became pretty "autistic" not gonna lie and probably I am annoying here or taking time. So I tried to see if indeed phases didn't matter for any two signals with different frequencies. So I sent some example. In which indeed 2Hz and 2.01 phase didn't matter indeed, but it was harder to prove it with different frequencies like 2Hz and 5Hz, with 3Hz and 7Hz I was able to show it (the peak was 1.19 but close enough), so I tried to deduce whether the phase really didn't matter and it will always be close to the peak value. Here I mean close or exact same value.
Close because at some point it repeats like in 3Hz and 7Hz where 21 cycles it repeats again so 1.19 is max and will never reach 1.25 but I was nitpicking. So I tried to generalize it.
But peak values etc are important I guess while making circuits.

 

[Averagesupernova]

This thread seems to keep morphing but I will not complain. I'll leave that to someone else.
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Concerning what changes when peak doesn't change and RMS does:
RMS is just what the acronym implies. The Root of the Mean of the Squares. It is a type of average. The value of RMS volts means that if you took that same voltage in DC the heating of a resistor would be the same with either voltage applied. RMS is not some made up word. Sample a waveform at say every degree for a full cycle. Square each sample, average them, then take the square root of the average. That's RMS. Do that with square wave and it should be obvious that RMS and peak are the same. Should clue you in what happens when an amplifier clips. Peak is limited, RMS continues to go up until the output is a square wave.

 

[Xenon02]

This thread seems to keep morphing but I will not complain.

Did I get it somehow correct with what I saw in post nr 159 ? And questions related to them as well ? I had some doubts when I was still scrolling the plotted figures.

Concerning what changes when peak doesn't change and RMS does:
RMS is just what the acronym implies. The Root of the Mean of the Squares. It is a type of average. The value of RMS volts means that if you took that same voltage in DC the heating of a resistor would be the same with either voltage applied. RMS is not some made up word. Sample a waveform at say every degree for a full cycle. Square each sample, average them, then take the square root of the average. That's RMS. Do that with square wave and it should be obvious that RMS and peak are the same. Should clue you in what happens when an amplifier clips. Peak is limited, RMS continues to go up until the output is a square wave.

Yea I can imagine RMS rising even if Peak is clipped.

 

[Tom.G]

For those that are interested, here is an interactive site that allows multiple plots on the same graph:

.https://www.transum.org/Maths/Activity/Graph/Desmos.asp

Cheers,
Tom

 

[berkeman]

Thread is paused for a bit...

 

[berkeman]

After a PM conversation, this thread will remain closed. The OP will be reviewing their previous Signals & Systems courses to bone up on this topic.

Thank you to all the patient helpers in this thread.