B How does output voltage of an electric guitar work?

[Averagesupernova]

I just wondered if the chord could just make the E1 reduced from 0.8V to smaller like 0.6V

If you actually did something besides pick stuff from the net that you really don't know what the signal is you would understand this. If you concern yourself with peak without considering RMS in this you will not get very far. Yes, adding a second signal from a different string could reduce the peak of the signal while increasing the RMS voltage.
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You need to study up on signals and systems to fully understand this. It's apparent that you don't. Yet you think you do.

If the above can be believed as accurate then the fact the RMS is higher with the chord vs E2 and the peak remained unchanged (20 mV to 36 mV RMS and 300 to 300 peak) should have answered your question, yet you asked. So that implies you don't trust the source of this info.
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It's really difficult to get anything meaningful about the behavior of the pickup just thumbing it. A constant vibration of the string(s) will tell you something. This has to be controlled and the travel of the string measured. This takes patience and a well fixtured setup.

 

[Drakkith]

It's really difficult to get anything meaningful about the behavior of the pickup just thumbing it. A constant vibration of the string(s) will tell you something. This has to be controlled and the travel of the string measured. This takes patience and a well fixtured setup.

Indeed. I've brought this up at least twice now and I would be very surprised if the numbers listed could be reliably replicated when playing by hand.

 

[Xenon02]

If the above can be believed as accurate then the fact the RMS is higher with the chord vs E2 and the peak remained unchanged (20 mV to 36 mV RMS and 300 to 300 peak) should have answered your question, yet you asked. So that implies you don't trust the source of this info.

Aha so indeed I was partly correct that the E2 was reduced because of the chord like you have said here (20mV to 36 mV RMS and peaks are the same 300mV) so the E2 peak had to be reduced then. But yea the RMS changed which I didn't give much thought. Well not always the peak was reduced but I get the idea.

Oke I think now I know what I wanted to know, now I can go back to the stuff that really matters ;>
I know this knowledge might be not useful but now knowing a bit how it looks like, satisfies my reptilian cerebellum.

Of course the source info isn't very accurate like it was said before, still thanks for patience. I'll just go back learn basics I guess ;>

You have, as I mentioned above, asked a question that really doesn't mean a lot. You are trying to run this process on your own terms, leaping in, half way through without taking on board the basics. Why do you think the answers you've been getting are not satisfying you? It's because you are trying to run before you can walk. You should try some other, very fundamental sources, like the basics of signals that can be found in a decent EE text book. Not the style of many, these days, I know; there are a lot of newbies who seem to think that the basics don't count. There are other forums that are chock full of nonsensical ideas about musical signals and processing. Very entertaining but not good sourses for getting a proper understanding

I mean learning from text books won't be something new to me ;>
But I will do what you've said. I've had before lessons about signals etc (hamm windows, white noise etc.), tbh I couldn't understand a thing ;>

So for this discussion I just researched how to analyse output music signals and it was mentioned the superposition. That every weird looking signal can be deconstructed into bunch of sine signals. So I used it in this case after some reading.

Still thanks for the help.

 

[Drakkith]

Aha so indeed I was partly correct that the E2 was reduced because of the chord like you have said here (20mV to 36 mV RMS and peaks are the same 300mV) so the E2 peak had to be reduced then.

I'm not sure that's what Averagesupernova meant.

 

[sophiecentaur]

Aha so indeed I was partly correct

Avoid being complacent about this. You have a long way to go still; as @Drakkith says, you may only 'feel' you are right.

 

[Xenon02]

I'm not sure that's what Averagesupernova meant.

Ok maybe yea it could be the possibility, but it's still a good thing to know this could be the thing.

Avoid being complacent about this. You have a long way to go still; as @Drakkith says, you may only 'feel' you are right.

I mean, I tried to link this with the theory I've read, and if it wasn't then the question was why focusing on mainly that point of where the math didn't math. So Hence I understood from Averagesupernova post that E2 having peak 300mV and the chord that consist of E2 + ther sounds also have 300mV could be like that because the chord (other sounds) could reduce the E2 peak voltage. There might be other reasons like maybe E2 that time was hit lighter than before or the string was further from pickup, or other factors you've guys provided.

So being complacent about something that was partly right is a good thing I guess ... Because the part about peak not adding up to the result and some speculations weren't wrong or atleast could be the thing why E2 and chord had the same amplitude while chord has E2 in him as well as other sounds that should add up. So this possibility is fine by me that could be possible.

Still thanks for the help and patience, but I felt unwelcome here at some point, so I'll just leave it this way. If again post 103 wrongly interpreted post 102 then I don't know what is true then ;> Because I really tried to show some stuff I found and focus on factors that didn't match but I felt like when I asked a question the answers where about something else ;D

 

[bobob]

Here is a great article that derives explains how a guitar pickup works in great detail.

http://kirkmcd.princeton.edu/examples/guitar.pdf

 

[sophiecentaur]

So being complacent about something that was partly right is a good thing I guess ... Because the part about peak not adding up to the result and some speculations weren't wrong or atleast could be the thing why E2 and chord had the same amplitude while chord has E2 in him as well as other sounds that should add up. So this possibility is fine by me that could be possible.

IF you have a hand-waving reason for thinking that your thoughts are in tune with reality then you may be allowing yourself to suspect that your 'understanding' is good. Using an arbitrary set of numbers for an argument doesn't get us anywhere because that can easily mask what could happen with different values. It would instantly destroy the possibility that 'understanding has occurred'.

could be like that because the chord (other sounds) could reduce the E2 peak voltage.

That doesn't make sense. The peak in one signal can always add (at a certain time)directly to the peak of a second signal. That doesn't necessarily apply for some combinations of signals that are harmonically related and with a constant phase relationship but no musical instrument behaves like that. Of course, those resulting peaks may not occur very frequently but you'd need to look at the statistics of any particular combination of signals.
Without some attention to the maths involved then all you can do (and it might be enough for many situations and satisfy you, personally) would be to read about other people's experiences, measurements and opinions. But don't be surprised when your own experience goes against what you thought you 'knew'. And don't be surprised when boring old nerds (PF members etc., like me) don't take you seriously because they learned it the 'proper way'.

They didn't manage to get the James Webb Space Telescope to work, a million miles from Earth, by not being rigorous in their theory.

 

[Xenon02]

That doesn't make sense. The peak in one signal can always add (at a certain time)directly to the peak of a second signal. That doesn't necessarily apply for some combinations of signals that are harmonically related and with a constant phase relationship but no musical instrument behaves like that. Of course, those resulting peaks may not occur very frequently but you'd need to look at the statistics of any particular combination of signals.

Sorry for long wait.
Then why peaks don't add this is still a mystery for me. Why superposition doesn't work ? The peaks of two sounds must add up at some point... If possible could you give me an example I can relate to then ?

I just see not much logic in it.
Yes I don't know what the input looks like. I only know some output example from the web. Yet I still got interested because the thought of "How people making sounds mixing know what will be the amplitude or if the instrument won't surpass that voltage and make it distorted". I know how distorted signal looks like so the sound is really different.

Without some attention to the maths involved then all you can do (and it might be enough for many situations and satisfy you, personally) would be to read about other people's experiences, measurements and opinions. But don't be surprised when your own experience goes against what you thought you 'knew'. And don't be surprised when boring old nerds (PF members etc., like me) don't take you seriously because they learned it the 'proper way'.

What is a proper way then ?
I just found something confusing and wondered how it was resolved.
Is it because I tried to learn it from websites ?

I've used stuff I learned like superposition, interference etc. And tried to apply to this example. I learned here that interference isn't applied to two different frequency signals but superposition yes. So I used a graphical website to see how it is. And I proved that peaks at some point must to add up. So adding all sounds should surpass the voltage yet it didn't. Hence it was weird for me.

PS.
As one person said that in example E2 and chord had two different RMS but the same peak should answer my question yet I tried to deduce something and I was incorrect so what is the correct answer I should take as a fact ? Why is it not distorted ? Why it doesn't add up ? Why it doesn't surpass a certain voltage level ? Why it is not necessary to understand not knowing the output of something that changes the input ? Same shape but different units. Why making a guitar effect its said that pickup is 0.7V peak so they make circuit around this value.
While single strings makes this huge of a peak and somehow never exceeds this peak value ...

Maybe some wicked math is behind of it, and my physics knowledge is 0, yet trying to understand it. Maybe I take some stuff happens at instant.

 

[sophiecentaur]

What is a proper way then ?

It should involve a text book or the equivalent on-line source. If you are relying on casual, ill informed remarks then don't be surprised when you get it wrong. If you are finding 'contradictions' in what you are taking on board, it's because you are either not reading good stuff properly or reading dodgy sources. None of what you are claiming to be inconsistent is actually not consistent. You have to be prepared to learn stuff and not to jump to your own conclusions after minimal reading. Don't expect any of this to be 'obvious'.

Then why peaks don't add this is still a mystery for me. Why superposition doesn't work ? The peaks of two sounds must add up at some point...

Of course "peaks add" but only when they coincide in time. No one has claimed that superposition doesn't work; it has to, in a linear medium.
If you are trying to relate the addition of non-related signals to Interference, (which is between coherent signals) then you will always be confused.
Your "PS" implies that you have not actually been reading what's in this thread. Peak and RMS values of two signals are not automatically tied together except when you are discussing the same signal (e.g. sine wave).

 

[Xenon02]

Of course "peaks add" but only when they coincide in time. No one has claimed that superposition doesn't work; it has to, in a linear medium.
If you are trying to relate the addition of non-related signals to Interference, (which is between coherent signals) then you will always be confused.

This is what I tried to say by using a two signals with different frequency that at some point the peaks must add up. If the two signals were the same frequency and had a small phase shift then their peaks won't add up ever, but this is a different story with two signals with different frequency.
But yea it is still confusing, looking at certain real values.

Your "PS" implies that you have not actually been reading what's in this thread. Peak and RMS values of two signals are not automatically tied together except when you are discussing the same signal (e.g. sine wave).

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. Yes they are not sinusoidal, but these signals consist of many sinusoidal signals. Hmm how to describe it so it won't sound stupid from me, any sound can be made adding up many sinusoidal signals so in fact even if the input is not sinusoidal it consist of many sinusoidal signals with different frequencies so they add up.
It's hard to imagine to be honest, is there any picture that could better describe what you've tried to tell me ? Sorry if I am asking alot.

I just see it in the way I saw in lessons like sinuses adding up or that every signal is like a bunch of sinuses added up to create a unique shape of a signal.

So I gave my thoughts and it was confusing in many ways, such as why 0.7 was max value (more renowned circuit designer in music assumed this in circuits I have seen made by him), if the strength of the strum can make the amplitude bigger then what is the limit ? why it doesn't distort ? Can strumming the string has a limit ?

Also why this question is also irrelevant ? I know in practical use designing a circuit probably I just need to know max value and that's it. But there are tools to reduce some specific frequency so it is known the value. These frequency has to be somehow picked and reduced. Or making a sound effect that affect I guess specific frequencies so I must to know how much to reduce etc. So it's cool that superposition works but somehow seeing real values it is just incorrect. I can't picture it why though. And what if I just strum to hard ? The amplitude could make the circuit just distort, or if even pickup can distort stuff. If only pickup distort before giving the signal to the circuit then it should be hearable even small cut will lead to distortion. Playing the same chord should lead to distort to if the sum is just to big.

It should involve a text book or the equivalent on-line source. If you are relying on casual, ill informed remarks then don't be surprised when you get it wrong. If you are finding 'contradictions' in what you are taking on board, it's because you are either not reading good stuff properly or reading dodgy sources. None of what you are claiming to be inconsistent is actually not consistent. You have to be prepared to learn stuff and not to jump to your own conclusions after minimal reading. Don't expect any of this to be 'obvious'.

The sources aren't that ill informed, I've gained some of these sources from people that tried to get me into it. But after learning or rather

 

[sophiecentaur]

What do you mean by not tied together ?

= low coherence

So there were 2 signals separate and 2 signals together at the same time. Yes they are not sinusoidal, but these signals consist of many sinusoidal signals

Describing the signals from the two strings as "many sinusoidal signals" is only describing them in the frequency domain, rather than in the time domain. The two descriptions are entirely equivalent. Neither is more correct than the other. If you are concerned with ampl.idier 'headroom' then the time domain description is more informative and relevant because it's when peaks on each signal happen to coincide in time that the cracking is heard.

So it's cool that superposition works

It's a fact that superposition is what happens in a linear system. That's hardly "cool"; it just is.

 

[Xenon02]

= low coherence

I still don't get this part or perhaps I don't know what coherence is or looks like in this situation.

something like this ? I mean yea it looks like they are of different frequencies so because of that the peaks must add at some point in time. All peaks visible in the incoherent part will add up at some point no matter what creating really big value of that peak.

So still I don't know what this has to this

Your "PS" implies that you have not actually been reading what's in this thread. Peak and RMS values of two signals are not automatically tied together except when you are discussing the same signal (e.g. sine wave).

So it still suits the idea, many signals with different frequencies adds up at some point all their peaks. In the reality it does not, question is why. If they do add up like with E1 and E2 it can exceed this 0.7V said while constructing a circuit. And why pickup doesn't distort it ? Or can pickup distort it/cut the signal or it will just give in the output 2V instead of 0.7V max.

If you are concerned with ampl.idier 'headroom' then the time domain description is more informative and relevant because it's when peaks on each signal happen to coincide in time that the cracking is heard.

Is it heard ? When you play many time the same chord or the same note, you won't hear the crack, when the smallest distortion happens (peak is just cut and flattened) then you hear the crack. Or at least that what I felt listening to many kinds of music and in real life as well.

So that's why I asked for any visualization. Because I see you understand my question and you know what it looks like so maybe you know an image or something that could show more. A picture is worth of a thousand words. Also tried to emphasize it or visualize my confusion at any point so far.

It's a fact that superposition is what happens in a linear system. That's hardly "cool"; it just is.

I just said that (it's nice that what others think is also correct to what I thought as well), nothing more behind of that "cool". And I don't know what you've tried to imply here. I was just glad that my part of thought was correct with others, I need to also emphasize that it is a part not the whole thing I wrote.

 

[Tom.G]

I don't play guitar, or any musical instrument for that matter, My background is mainly in electronics (with bits from other technical fields). I'll likely get a few details 'not quite right' but most of it should be close.
That said, lets try this.

"Why doesn't it distort?"

A)
As I understand a guitar pickup, it is a coil of wire wound around a permanent magnet. A wire will have a voltage induced in it if it is in a changing magnetic field. A coil of wire will have that voltage induced into each turn; with the induced voltages from each turn adding to each other.

Even though it isn't a magnet, the string of an electric guitar is made of a material that is magnetic; that means it can be magnetized and will also be attracted to a magnet.

When that guitar string is near a magnet it distorts the magnetic field around the magnet. If the string is vibrating, the magnetic field around the magnet will change with the vibration. For a given motion the amount the field changes depends on how close the string is to the magnet.

B)
That coil of wire around the magnet will have a voltage induced in it by the changing magnetic field. The amount of voltage will depend an the field strength, how close the string is to the magnet/coil, and how fast the string is vibrating (what note it is playing). WIth this setup, the only way to get distortion is if the string contacts the pickup. If the string hits the pickup, it is not moving for an instant, no changing field, no output voltage (in other words, the output waveform would have a notch in it.)

C)
This is where I make the assumptions that:

1) the 'nominal' output voltage from the pickup coil would be measured at a 'standard' distance between the pickup and string,
2) while playing a specific note,
3) and that the string is made with a 'standard' material.
​

D)
Given the above assumptions, the pickup could be designed to give a specific output voltage at 'standard' conditions; perhaps 0.7V.

Now none of the above says anything about the maximum input voltage the amplifier can handle without distortion. Since amplifiers do have volume controls, their gain can readily be adjusted to handle a wide range of input voltages without distortion. If you want distortion, use a Fuzz Box.

Hope this helps!

Cheers,
Tom

ADDENDUM: That "coil in a changing magnetic field" is the the basis for power at the wall outlet at home, and the alternator in a car that keeps the battery charged.

 

[sophiecentaur]

@Xenon02
You will have seen many different pictures of waveforms. The 'spikey' sounds from a guitar string have a waveform with distinct peaks - unlike all your smooth, sinusoidal examples. Two similar waveforms of that sort of shape will clearly only cause an audible crack then the peaks occur at the same time and add together. That is far more obvious than the subtle changes

in 'roughly sinusoidal' waves. An amp may produce very little distortion except where the spikes on two waveforms occur at the same time.

it's nice that what others think is also correct to what I thought as well)

Don't assume that this is anything more than chance - if you don't understand the theory. Theory is not 'thinking'.

When you play many time the same chord or the same note, you won't hear the crack

How would you actually identify the 'crack'? The distortion will be more audible as the amplitude is increased but you can only be sure of detecting it if you subtract the original waveform from the new one (suitably scaled). Your ear can't do that but distortion measuring equipment effectively does just that.
But I have already remarked that all musical instruments produce distortion all the time so you cannot be certain of what you are hearing.

And why pickup doesn't distort it ?

What evidence do you have? Theory will predict distortion but that doesn't mean you will hear it in mild cases.

A)
As I understand a guitar pickup, it is a coil of wire wound around a permanent magnet. A wire will have a voltage induced in it if it is in a changing magnetic field. A coil of wire will have that voltage induced into each turn; with the induced voltages from each turn adding to each other.

Unfortunately there is another can of worms here. It could further confuse the OP.
1.The induced voltage will be proportional to the rate of change of flux. So it's already differentiating the position of the string related to the pole.
2. The fields around the pickup are not uniform where the string is moving about, by any means, so large displacement of the string will take it through a range of magnetic field values (and directions).

I was hoping to avoid these extra complications which tell us that the 'transducer' is not actually linear. That will mean the signal from each string is a 'version' of the basic note (distortion of the individual signals).
However, inside the pickup, the system is linear so the individual emfs will add in a well behaved fashion so there would be little cross-modulation between the individual signals.

 

[Xenon02]

You will have seen many different pictures of waveforms. The 'spikey' sounds from a guitar string have a waveform with distinct peaks - unlike all your smooth, sinusoidal examples. Two similar waveforms of that sort of shape will clearly only cause an audible crack then the peaks occur at the same time and add together. That is far more obvious than the subtle changes

in 'roughly sinusoidal' waves. An amp may produce very little distortion except where the spikes on two waveforms occur at the same time.

May I ask if I can.
So I understand that this picture is like a single string sound. I can imagine it is like that. This can be also analyzed as many sinusoidal signal added up into this red signal.

Also my signal I know it was clear sinusoidal but the sum was not. So my point was that the peaks should add up.

So I understand that the peak of red signal and the second signal very similar to the red signal must add up at some time, hence the time is small that even if the distortion happens we don't hear it ?

That's how I understood the text

How would you actually identify the 'crack'? The distortion will be more audible as the amplitude is increased but you can only be sure of detecting it if you subtract the original waveform from the new one (suitably scaled). Your ear can't do that but distortion measuring equipment effectively does just that.
But I have already remarked that all musical instruments produce distortion all the time so you cannot be certain of what you are hearing.

Okey that's how I understood the text :

- the sum of peaks happens
- these peaks will produce the distortion but it is not hearable
- it is hearable if it more distorted or longer ?

The problem I also have is how big value can the input give and how the pickup produces the output (I know changed in magnetic field) but how strong the vibration must be to achieve 0.7V peak etc. The distance matters etc as I read.
Maybe I slowly get it I dunno for now I am said to "have" a feeling of understanding then I don't know what is learning when I ask questions, try to use my own words to confirm if this is what you meant :D

Still thanks.

 

[Averagesupernova]

@Xenon02 you are assuming that the signals that make up the complex waveform are all as large as the signals in your sine wave example. This is not the case.
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Yes, signals add. Yes, the amplifier will clip if the signal gets large enough. No, you cannot always hear this and if you do it might not sound like something you think is wrong.

 

[sophiecentaur]

@Xenon02
You will have seen many different pictures of waveforms. The 'spikey' sounds from a guitar string have a waveform with distinct peaks - unlike all your smooth, sinusoidal examples. Two similar waveforms of that sort of shape will clearly only cause an audible crack then the peaks occur at the same time and add together. That is far more obvious than the subtle changes
View attachment 350636
in 'roughly sinusoidal' waves. An amp may produce very little distortion except where the spikes on two waveforms occur at the same time.

it's nice that what others think is also correct to what I thought as well)

Don't assume that this is anything more than chance - if you don't understand the theory. Theory is not 'thinking'.

When you play many time the same chord or the same note, you won't hear the crack

How would you actually identify the 'crack'? The distortion will be more audible as the amplitude is increased but you can only be sure of detecting it if you subtract the original waveform from the new one (suitably scaled). Your ear can't do that but distortion measuring equipment effectively does just that.
But I have already remarked that all musical instruments produce distortion all the time so you cannot be certain of what you are hearing.

And why pickup doesn't distort it ?

What evidence do you have? Theory will predict distortion but that doesn't mean you will hear it in mild cases.

So my point was that the peaks should add up.

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.

Maybe I slowly get it I dunno for now I am said to "have" a feeling of understanding then I don't know what is learning when I ask questions, try to use my own words to confirm if this is what you meant :D

The best level of understanding is when you can predict what will happen in a particular situation and it turns out that way. In this sort of subject it has to involve some formal maths and is verified by an experimental result. (Alternatively you can deal with 'set' questions in the book and get the 'correct' answers.) That avoids the risk of a false feeling of understanding. None of this stuff is a matter of opinion - any more than your three times table.

 

[Xenon02]

@Xenon02 you are assuming that the signals that make up the complex waveform are all as large as the signals in your sine wave example. This is not the case.
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Yes, signals add. Yes, the amplifier will clip if the signal gets large enough. No, you cannot always hear this and if you do it might not sound like something you think is wrong.

Yea you are right. I just assumed that signals can be large from the website I was referring to so that's why I think I asked how input looks like or how big it can be so that pickup changes this input into equivalent voltage output. And I thought pickup only makes 0.7V but it can make more if the peak of two signals is big.

It's a shame that peaks in the website I've provided their sum didn't match up with my expectations for some reasons. Maybe the peak wasn't "visible" at that vast time.

And ok so the do clip but it is not hearable, for it to be hearable probably the distortion has to occur more often or something or last longer.

 

[Averagesupernova]

Yea you are right. I just assumed that signals can be large from the website I was referring to so that's why I think I asked how input looks like or how big it can be so that pickup changes this input into equivalent voltage output. And I thought pickup only makes 0.7V but it can make more if the peak of two signals is big.

It's a shame that peaks in the website I've provided their sum didn't match up with my expectations for some reasons. Maybe the peak wasn't "visible" at that vast time.

And ok so the do clip but it is not hearable, for it to be hearable probably the distortion has to occur more often or something or last longer.

Sometimes it may clip, others not.
-
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.

 

[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?