Hearing frequency?

Hmm... do you know for a fact that it does? From what I know (which is limited), a tone is either audible or not; if it's audible, one hears pulses if it's a pulsed tone and a steady tone if it's steady. Otherwise, you just don't hear it. (I.e. a pulsed tone can go into a frequency higher than you can hear, and then you stop hearing it but it doesn't become steady.)

You are misunderstanding what I mean by frequency. I do not mean the pitch frequency. I'm talking about the number of pulses per second, ie. the frequency of pulses. At some point the ear will fail to discern the pulses. I'm sure of that, I just don't know what the threshold is.

Oh, OK.

I dunno.

Human ears are extremely variable, and I'd tend to doubt that it's one objective threshold that holds true in general. I think it's more likely that some people would be able to discern discrete pulses after others say that it is a steady tone.

But I dunno.

Soz is probably correct that it varies from person to person. It does with light. Some people are just fine with flourescents and others are driven crazy by the cycling on and off of flourescents.

If I were to make a guess I would think when it comes to sound pulses the threshold needs to be less than cycle for the lowest audible sound. This raises the question of is the audible pulse cycle different for different sound frequencies? I would suspect it might be but don't have any information to support it. Interesting question though.

Ok, so perhaps "frequency" was a poor choice of words since it's apparent that it confuses people. My question is how many beats per second can a human ear detect?

You are wrong about the lights. Human eyes can only detect pulses less than about 30Hz (30 pulses per second). This is why movies are shot at 29.97 frames per second. At that rate, the movie seems continuous. We are unable to detect the changing of frames. This is exactly what I am talking about.

Most digital sound files are sampled at 44100Hz (samples per second). They seem continuous. I want to know at what point, how many samples, we would detect the break between them.

Its not the same between two different individuals. A pulsed tone involves the acoustical physics of beat frequencies and they are dependant on the fundamental frequency of the audible tone. The subject becomes even more complex when you play around with the pulse duty cycle and/or the ADSR envelope (Attack, Decay, Sustain, Release).

I will take the liberty of rephrasing the question in an unambiguous manner.

At what ratio of duty cycle does a perfect square wave of a fixed frequency audible tone become indistinguishable from a perfect sine wave of the same fixed frequency ?
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.
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Actually in rephrasing that question the answer has become apparent.

You will always be ale to perceive the difference and the reson is this :

A pulsed tone is usually some form of square wave. Square waves and their variants have harmonics generated at even multiples of the fundamental frequency all the way up and down the spectrum. You can hear these higher harmonics.
A sine wave is a pure tone without harmonics. Your brain perceives this as being very different to a square wave.

There is another factor regarding the square waves and their duty cycle.
If you start with a 50:50 duty cycle or the traditional square wave and then start to increase the duty cycle the increase will make the square wave less of a square wave and it's waveform will head towards either the maximun or minimum DC value depending upon which way you decided to alter the duty cycle. It will start to become a glitch waveform which is very far indeed from the sound of a sine wave.



When you alter the duty cycle to it's extreme you reach one of the DC levels of the waveform and then there is no variance in the signal and thus nothing to hear because the speaker cone isn't moving anymore. It is merely stuck all the way out or all the way in and you hear nothing.

So the answer is that you will always be able to tell the difference but the closest to the perfect sine is a perfect square wave and you can easily distinguish those.

That woke me up.

Oh and to eliminate any possible confusion here...

It doesn't matter how many pusles per second there are. You will still be able to tell that they are pulses until the frequency goes above or below the limits of your ears' and brain's frequency response.
And then you can't hear them anyway.

I think the confusion in the original questionw as due to the assumption that : "sine waves are made up of little bits which are sort of like square waves or pulses so as long as you have many many pulses that should total up to the sine wave.
Sort of like the infinite number of chunks you divide things up into when you're doing calculus so the sum of the bits equals the whole. Right ?"

Wrong.

Sine waves and square/pulsed waves are fundamentally different.
Sines have no harmonics, squares do.

Now I need another cup of tea and some Marmite toast.
Yummy.

OK. I got one....

If a tree falls on a bear and it farts as it is being crushed to death and there is no one else around to smell it, is there any evidence that the bear had a history of obsessive compulsive disorder?

If there is no one else around to smell it then this implies that there are no observers at all.
Therefore the tree falling or not falling remains in a superposition of states thus the bear cannot either fart or not fart until information from the system is exchanged with an observer who can collapse the quantum wavefunction and thus observe either one state or the other.

In either event a simple examination of the bear's medical records will reveal any history of obsessive compulsive disorder.

:wink:

Thanks for the detailed explanation, Heliotrope.

No worries.

I have a question concerning your reasoning heliotrope.

Pulses of sound are not square waves, rather they are the starting and stopping of sine waves. Can you create sound at all without a complete wave? If you shorten the sound pulses so they aren't a complete sine wave are they still sound? A high pitched sound cycling 3 times a second would actually contain several sine waves each time it is on.

If you make the pulses a given length and the silence a given length as you make the silences shorter and shorter without changing the length of the sound you can eventually create a continuous sine wave.

I'm not even sure you can drive a speaker to make any sound without a complete sine wave. From resting position, out, in, to resting position.If your pulse is a complete sine wave as you remove the silence you would create a complete sine wave.

Nothing wrong with my reasoning.


Sound can be made up of any kind of wave you like.
Square, sine, triangular and irregular wafeforms all sound like sound and all sound differently.
You really need to hear them and look at them on an oscilloscope to appreciate the differences. If you can do that great.
If not then just have a look around the web at one of the more respectable encyclopaedias to see what the details are.


Nope. That's pulsed sine waves. Same as an RF (radio frequency) pulse. That 10 microsecond pulse contains many complete cycles of a 100 megahertz frequency.
See the pic I've made for an example.


Yep.
It's very easy.
In fact you create chopped up sine waves all the time when you use the dimmer switch on your house lighting. The circuit in there just chops off the sine wave at a time determined by the setting of the knob so you get more or less energy into the bulb so it brightens and dims as you turn it.



The problem with this is that (let's go back to sound rather than 50Hz electricity here) if you play your chopped up sine wave you get some pretty sharp changes in the waveform. Sharp edges.
Like in the diagram.
I've put in some dotted "lines" to show where the waveform would have gone if you hadn't hacked it all to pieces with your clever dimmer circuitry.
Now those sharp edges are a lot like square waves.
Square waves have lots of higher harmonics associated with them.
I said earlier that they were even harmonics. I was half asleep as it was early. They're actually odd harmonics.
So if you play this waveform through your speaker it will not sound like the nice pure tone of a pure sine wave. It will have distortion. It will sound harsher. It will have some audible nasties in there.
So it sounds different.


That's actually not a high pitched sound.
3 cycles per second or 3 Hertz is actually a very, very, very low pitched sound.
So low in fact that it's well below the frequency you can hear sound at.
It's called Infrasound.
Humans generally can hear between 20 cycles per second (20Hz) and 20,000 Hz (20kHz).
Only whales or massive dinosaurs or weird people can hear at 3Hz.
Actually your brain's Theta Waves are about 3 or 4 Hz but they're electrical so you can't hear them anyway.

I think you really meant 3 pulses per second, each perhaps containing several full cycles of a say, 1kHz wave. Like the pulsed sine wave above.
That would sound like a beep noise.
A beep is a pulsed sine wave.
Now change that pulsed 1kHz sine wave into a square wave and it sounds similar but it has many odd harmonics so it sounds harsher and more ragged. It's still a beep though.


True.
But only if you're using the pulsed sine wave.
If you're using the pulsed square wave all you get is a continuous square wave.


Of course you can.
It's dead easy.
It will just be distorted that's all.

Got an old speaker hanging around anywhere ?
Something from a crappy old PC for example ...
Anyway, get the speaker and take the wires and put them across a 1.5V battery. A double-A (AA) pencil cell from a Mini-Maglite or something will do.
Watch the cone of the speaker when you touch the battery to the speaker wires.
It doesn't matter which way around you have the battery but you can turn it around to see what happens.
Put one wire on the positive and the other on the negative terminal of the battery. Then swap around and see what you can see.
Also try keeping one end on with your finger and then rapidly touch the other wire to the other end of the battery and watch the speaker again.
Keep your ears open when you're doing this too.

Have fun !

Interesting stuff, Heliotrope!

Heliotrope.

Square waves are easy to produce in electrical circuits. I understand that.

Square waves don't translate well to sound transmitting through the air.

There is no on/off in air movement any more than you can get perfectly square waves at the ocean. When you drive a speaker you don't go from instantly in to instantly out. There is a mechanical factor as the speaker moves from one position to another. You can create longer peaks but there is no true squareness to them. It might look like a square wave if you use the right scale but as you increase the scale you will see a curve of some kind moving from the low to the high position. The harmonics are probably a result of that movement.

Yes, I meant high sound on/off 3 times a second.

If you use a triac to dim lighting you are creating a period of time that the light is off. I don't know if that works the same way in sound. Remember the cut off sine wave only reflects the electricity traveling to the lamp. It doesn't truly reflect the light being output. The filament will have a warming and cooling period which is probably why we don't see a more visible flickering as the light is dimmed.


To go back to the original question on the thread. A pulse of sound requires almost the full sine or other wave in that pulse to be a sound. In order to hear a pulse it has to contain sound. Since the sound has to be a sound and the silence between it is a silence I don't think you can use just a single wave to represent how it will act. If you are producing a 1000htz square wave there is no silence between pulses that is audible. That is why I originally suggested that the silence can't be the same length as the sound. Imagine a 1000htz sound that is cycling at a 300htz rate. When you do that, you are probably not hearing silence because the 300htz is creating a harmonic.

Good stuff.
You've got the basics then.


Depends exactly what you mean. I'll get to that later.


True.


True.


Well the bottom line if you want to get really nit-picky about it is that there is no true squareness to any waveform. It is impossible to change state in zero time therefore there can be no true square waves of any description.
However, we do live in the real world and not in an ideal universe and so do our ears.


True.
That change from the low state to the high state or vice versa takes a finite amount of time. It is called the slew rate. It must therefore have a slope. It cannot slow down instantaneously to a stop and so therefore there must also be a curve when it does so.

The point is that these curves are almost non-existent. You need a really spectacularly powerful oscilloscope to see them when you have a serious square wave generating circuit at your disposal.
I'll give you an example from something I built years ago for a project I was playing with.
I used a chip that was generating square waves for use in a reference distortion measurement. That chip was an operational amplifier. The OpAmp I chose was able to change state between minium and maximum output very quickly indeed. I hasten to add that this is/was a commercially available part you can pick up for a few pennies at any Radio Shack store.
It's slew rate was, as I recall, about 50 Volts per microsecond.
That's 50 million volts per second it was capable of increasing it's output at.
So for a 1kHz audio square wave at a line output level suitable for driving a small speaker or a large amplifier, with a 50:50 duty cycle, basically a perfect square wave; this OpAmp can go from zero volts to the line level of 1.2 volts in about 25 nano seconds.
OK now factor in some in circuit garbage and reduce that by a factor of 10. Or even 20 if you like. It's still min to max in 0.5 microseconds.
A fairly basic 'scope will show you that easily but you'll need some hardcore equipment to see any sort of curve on the waveform edges.

So yes, you will see some curving of the waveform but if you reckon you can hear that then you have better ears than I.
And better ears than every creature that has ever existed on this planet.


Nope.
The harmonics are due to the fundamental properties of changes in state. Doesn't matter if it's electrical or anything else.
It's the edges that create the harmonics.


Still not sure what you mean.
'high sound' ?


True.
It's so small a time interval that you can't see it.
Remember the TV ?
That's 25 full frames per second or 50 interlaced frames per second. Your brain has a property that allows fast moving images to have a bit of persistence and so you see the individual frames as a single smooth stream of motion.
If something appeared on your screen for less than say, a two hundredth of a second you would never see it because you as a human are not capable of seeing things that happen in that sort a time span.

Same with the light.
It is completely switched off for a couple of thousandths of a second.
It flickers.
You can't see the flickering because you can't perceive time intervals that short.


It does.


Incorrect.
The electricity going to the lamp is what makes it light up.
'lecky flowing in one direction makes it light up. When the 'lecky stops the light switches off. Then the 'lecky flows back the other way and the light comes back on again.
This happens 50 times per second in the UK. 60 times per second in the USA.
This is the frequency of the mains voltage.
50 Hz UK, 60Hz USA.

Have you ever looked at a flourescent tube out of the corner of your eye ?
You can see it flickering because your peripheral vision is attuned to seeing things that move quickly. You can't see the flicker when you look straight on at it because that part of your visual system is attuned for high resolution not fast updating.


True.
That heating and cooling hysteresis (delay) is why the incadescent light bulbs don't appear to flicker.
This heating has nothing to do with the wave form of the electricity flowing through it but is a secondary effect caused by the filament dissipating energy as heat and light due to it's internal resistance .


Incorrect.
Go back and read what I wrote.


Incorrect.
The pulse does not contain sound.
The pulse contains electrons which flow through a coil of wire which has been wound onto a paper former which is then shaped around a magnet.
The flowing electricity (the electrons) creates it's own magnetic field which then interacts with the static field of the main magnet. This interaction causes the paper former and attached coil to move in response.
The paper former is attached to a paper cone which allows it to move large quantities of air which creates longditudinal waves of varying air pressure which impact upon your eardrums and cause it to move in sympathy.
The nerves in your ear take these movements and convert them back into electricity which your brain then interprets as sound.


This is circular logic and has no relevance.
Again, go back and read what I wrote.


You really really need to go and look at how sound works.


This is nonsense.
It's like saying "imagine a car that is travelling at 50mph that is travelling at 20 mph".


Is it just me or can you not hear silence anyway because it's errr... Silence ?
If there were harmonics you'd hear them and there would be no silence.

You seem to have some fundamental misonceptions regarding how pulsed waveforms work and what the difference between frequency, pulse width, duty cycle and pulse period are.
Get a hold of some books or run your browser through Wikipedia and see for yourself.
Get some information. Do not assume things.
Be ready to have your current understanding changed by the facts of how this lot works.

I have no intention to patronise you here or talk down to anyone. The basic fact is that I honestly don't have the will or the time to explain everything about this to someone who will not go and educate themselves and then ask pertinent questions.
So, go read the stuff and then if you have questions I will attempt to amswer them to the best of my abilities.

Remember : There is no such thing as a stupid question. Only stupid answers.