Does current have a frequency

[Hv&Lv]

It is possible in concept for the frequency of current to be different than the frequency of the voltage. You would need a kind of load that distorts the shape of the voltage waveform for this to happen. Usually, there is at least some kind of relationship between the current and voltage waveform frequencies. A circuit may also attenuate, or amplify a certain range of frequencies, or it may produce harmonics of the original fundamental. I can't think of any example that would produce completely different frequencies, that aren't directly determined by the frequency of the voltage waveform.

As an example, an ideal full wave rectifier will turn a simple sine wave of voltage, V(t)=sin(ω*t), into the following Fourier series, when applied to a unit resistance load:
View attachment 2571201

This is what the circuit looks like, with the load resistor being 1 ohm:

Here's a plot that shows how this evolves as more cosine waves are added (I've deliberately drawn offsets, so you can see them separately):
View attachment 2571202

For an ~0.16 Hz voltage source, the original ω=1 rad/s. Constructing the first few terms of this sum:
I(t) = 0.6366 - 0.4244*cos(2*t) - 0.08488*cos(4*t) - 0.03638*cos(6*t) - 0.02021*cos(8*t)

This produces all kinds of different frequencies from the original 0.16 Hz. First being 2ω, then 4ω, then 6ω, and so forth. But they are all whole multiples of the fundamental (ω), and are all related to it. The current has frequencies of 0.32 Hz, 0.64 Hz, 0.96 Hz, etc, while the voltage only has an 0.16 Hz frequency.

When I somehow managed to pass the class on Fourier transform / series I hoped to never use it again…

 

[ggunn]

When I somehow managed to pass the class on Fourier transform / series I hoped to never use it again…

This. Knowing that Beethoven's Fifth Symphony in C minor can be expressed as a Fourier series is an interesting fact, but working out the math is another thing altogether.

 

[Carultch]

When I somehow managed to pass the class on Fourier transform / series I hoped to never use it again…

You've probably use it a lot more than you realize. When you model impedances as Zl = j*ω*L, and Zc = 1/(j*ω*C), the working principles behind the scenes are that you're ultimately solving the differential equation that governs the circuit, with the Fourier transform. When everything is just sine & cosine waves of the same frequency, solving the diffEQ in the steady state, turns into algebra with complex numbers.

 

[GoldDigger]

The small vocal group at my undergrad school (Carleton College) was called the Overtones.
The rationale for the name was that the quality of a musical sound is dependent on the number of overtones present.

 

[LarryFine]

I learned about overtones when I sang in a quartet in school.

 

[Geber]

I found a video that shows various wave forms graphed in time, and in a different graph, as harmonics. It also plays the wave forms as sound. Just ignore all the talk about music synthesizers.

 

[ggunn]

The small vocal group at my undergrad school (Carleton College) was called the Overtones.
The rationale for the name was that the quality of a musical sound is dependent on the number of overtones present.

And then there are "ghost tones". If you are a guitar player, play a D chord in the first position. Now lift your finger from the high E string and play it again with the open E; it is a D9 chord with that E in it. Now kill the E string and play the chord again with the E string silent; you will hear that E in the chord even though it isn't there. The other notes you are playing beat on each other to create that high E even though you are not playing it.

 

[winnie]

Here is a fun video related to Fourier transforms. Instead of taking the sum of sine waves to make a periodic function, it takes the sum of various circular paths (epicycles) to create a picture:

 

[wwhitney]

And then there are "ghost tones". . . The other notes you are playing beat on each other to create that high E even though you are not playing it.

Is this a human perception phenomenon--if you hear frequencies 2k, 3k, 4k, etc then you think you hear frequency k even when it's not present?

Cheers, Wayne

 

[LarryFine]

Is this a human perception phenomenon--if you hear frequencies 2k, 3k, 4k, etc then you think you hear frequency k even when it's not present?

I'd say no, because it doesn't depend on it being heard; harmonics are real, recordable, and measurable.

 

[wwhitney]

I'd say no, because it doesn't depend on it being heard; harmonics are real, recordable, and measurable.

That I understand, my question was really "is the guitar making the fundamental frequency when doing what you described"? Because I don't know anything about guitars and couldn't follow the description.

My understanding of "ghost tones" is that if you tell a computer, for example, to generate all the overtones / harmonics but leave out the fundamental frequency, human perception "fills in" the missing fundamental frequency and you "hear" it even though it's not there.

Cheers, Wayne

 

[LarryFine]

That I understand, my question was really "is the guitar making the fundamental frequency when doing what you described"?

Yes, I believe so.

 

[jaggedben]

Yes, I believe so.

I agree. To the extent I recognize what ggunn is describing, I always thought that it was simply my movement of the guitar as I play that causes all open strings to vibrate even if I don't strum them.

 

[wwhitney]

Yes, I believe so.

OK, thanks. I was wondering if ggunn was describing a "missing fundamental" phenomenon, but apparently not.

Missing fundamental - Wikipedia

en.wikipedia.org

Cheers, Wayne

 

[ggunn]

I agree. To the extent I recognize what ggunn is describing, I always thought that it was simply my movement of the guitar as I play that causes all open strings to vibrate even if I don't strum them.

No, that is not what is going on; it happens when the E string is deadened so that it cannot ring. It has to do with beat frequencies generated when different notes are played simultaneously. The frequency of a beat between two notes is the difference in frequency between them; if you play 440Hz tone at the same time as a 441Hz tone you will hear a 1Hz beat. If you move the tone frequencies farther apart, the beat frequency increases, and if you keep moving them apart, at some point the beat frequency gets high enough that it is contributory to the chord. It is the auditory equivalent of a Moire pattern. I figured this out long before I became an engineer.

Aside: when I was in engineering school in an electromagnetics class, a test question was about an antenna that was broadcasting two slightly different frequencies simultaneously. The question was: at a point in time when the waves are both at their maximum at the point of origin, at what distance from the antenna would they also both be at their maximum. Everyone else in the class answered it with equations; I wrote a short essay. I said that the beat frequency generated between the two fundamentals would propagate at the speed of light just as the fundamentals did, so the distance was simply the wavelength of the beat frequency. My prof called me into his office and we talked about music.

 

[jaggedben]

No, that is not what is going on; it happens when the E string is deadened so that it cannot ring. It has to do with beat frequencies generated when different notes are played simultaneously. The frequency of a beat between two notes is the difference in frequency between them; if you play 440Hz tone at the same time as a 441Hz tone you will hear a 1Hz beat. If you move the tone frequencies farther apart, the beat frequency increases, and if you keep moving them apart, at some point the beat frequency gets high enough that it is contributory to the chord. It is the auditory equivalent of a Moire pattern. I figured this out long before I became an engineer.
...

Consider me skeptical that the other notes in the first position D chord have a beat frequency that produces that high E note. You might have to spell out the math for me. Also I've never noticed that in my decades of guitar playing.

 

[ggunn]

Consider me skeptical that the other notes in the first position D chord have a beat frequency that produces that high E note. You might have to spell out the math for me. Also I've never noticed that in my decades of guitar playing.

Try it and listen for the E that you aren't playing.

 

[synchro]

The frequency of a beat between two notes is the difference in frequency between them; if you play 440Hz tone at the same time as a 441Hz tone you will hear a 1Hz beat.

I believe that for small frequency differences you are mainly hearing the "envelope" of the sound waveform, which is the amplitude of the waveform as a function of time. This envelope will vary at the difference frequency of 1 Hz in the example above as the two tones alternately reinforce and cancel each other over a 1 second period. For larger frequency differences, a nonlinearity (such as a second order distortion) can create tones at the sum and difference frequencies There can also be tones due to intermodulation, for example at 2f₁-f₂ and 2f₂ -f₁ from third order nonlinearities, as well as higher order nonlinearities.

Apparently the difference frequency tones (known as Tartini tones) can be due to nonlinearities in the instrument or sound chain (sometimes intentional), or in the human ear itself when the sound level is sufficiently large.

https://www.animations.physics.unsw.edu.au/jw/Tartini-tones-temperament.html

 

[ggunn]

Consider me skeptical that the other notes in the first position D chord have a beat frequency that produces that high E note. You might have to spell out the math for me. Also I've never noticed that in my decades of guitar playing.

Omigosh, you're right; I am confusing two different things that I haven't thought about in a long time. The beat frequency thing is contributory to the way chords sound the way they do; for example, an A440 beats against an E660 at 220Hz, which is an octave below the fundamental and one reason why "power chords" (open fifths on the lower strings) sound so fat and why many metalheads tune their E and A strings harmonically to each other rather than to the tempered notes.

The D chord thing works best with new bright acoustic guitar strings, i.e., with a lot of harmonic content; the E I am hearing is the second harmonic of the A's in the chord. Two different things. Thanks for rattling my aging brain.

BTW, how many decades of guitar playing are you talking about? For me it is six, although to hear me play you probably wouldn't believe that I have been playing that long.

 

[jaggedben]

Omigosh, you're right; I am confusing two different things that I haven't thought about in a long time. The beat frequency thing is contributory to the way chords sound the way they do; for example, an A440 beats against an E660 at 220Hz, which is an octave below the fundamental and one reason why "power chords" (open fifths on the lower strings) sound so fat and why many metalheads tune their E and A strings harmonically to each other rather than to the tempered notes.

The D chord thing works best with new bright acoustic guitar strings, i.e., with a lot of harmonic content; the E I am hearing is the second harmonic of the A's in the chord. Two different things. Thanks for rattling my aging brain.

That makes a lot more sense to me.

BTW, how many decades of guitar playing are you talking about? For me it is six, although to hear me play you probably wouldn't believe that I have been playing that long.

For me it's three, and your last comment equally applies.