[odigg]

I've been thinking about how human hearing works and I've hit one of the "What" moments.

Hopefully somebody can help.

Final questions in brief: How is it we can hear different frequencies simultaneously? How is it a driver can produce sound in such a way that it sounds like we are hearing different frequencies simultaneously?

The above question, just in much more detail:

First, let me describe my understanding of a driver. Perhaps I'm thinking about it incorrectly and this is my problem.

A driver moves air. A driver does this by vibrating. It vibrates faster for higher frequencies and slower for lower frequencies. A driver cannot vibrate in such a way that it produces two frequencies at exactly the same time (eg. 100hz and 10000hz). A driver can only vibrate at one frequency at a time.

So let's say we have a flute (high frequencies) playing with a cello (low frequencies). Each instrument is producing a particular waveform. When you record these instruments playing, the microphone picks up one complex waveform. This complex waveform is a composition of the flute and cello and only has one frequency (the combination of the flute and cell at that moment) at a given moment.

Thus the driver has to only reproduce one frequency at a given moment.

But if this waveform is a combination of two instruments, how can I tell them apart when I hear them? Why do I hear two instruments and not just one instrument that sounds like a combination of a flute and cello? Is it because the waveform/frequencies is changing quickly the brain figures it out? It is like a movie, where the brain sees individual pictures as fluid motion?

Hope all this made sense.

 

[Gamerphile]

In a simpel answer its because the ears only pick up one complex waveform too in a very similar maner as a mic. So the hole ear structures and related brain parts split this into many different peices and reconise them in many different ways like where the sounds are comming from in relations to the listner and what frequncy etc.

 

[stevenkelby]

The driver does produce two frequencies at once. Imagine a driver moving back and forth at 10,000 Hz. While doing that, imagine it also moving back and forth at 100Hz. It can do both at the same time.

Your ear does the same thing in reverse, several frequincies at exactly the same time, one on top of the other.

 

[odigg]

Quote:

Originally Posted by stevenkelby /img/forum/go_quote.gif The driver does produce two frequencies at once. Imagine a driver moving back and forth at 10,000 Hz. While doing that, imagine it also moving back and forth at 100Hz. It can do both at the same time. Your ear does the same thing in reverse, several frequincies at exactly the same time, one on top of the other.

How is this possible? My understanding of a driver is that it works like a piston, and my best understanding of a piston is from a car engine as I'm more familiar with engines than I am a transducer.

A piston in an engine cannot move at two speeds at the same time. Even if the piston in the engine weighed almost nothing and had no inertia, it could still not move at two different speeds simultaneously

I guess I can see how a magnet can send out a 10Khz frequency from the center of the driver, then before the 10Khz reaches the outside edge the magnet starts vibrating at 100hz.

But this isn't happening simultaneously in the magnet, and it hasn't happened simultaneously over the whole driver either. One frequency did come before the other, even if they can mix in the middle. Does this make sense?

 

[ThePredator]

Look up "composite waveform". What is happening is the waves are interfering to create a single more complex wave that is broken down again by the brain.

A picture of a waveform:

 

[stevenkelby]

If you were here I could show you with my hands but its hard to explain! I'm not very articualte at the best of times. I'm not an EE or anything but this has been explained to me well.

I know what you mean and I used to think the same way. A driver is like a piston only in the sense that the motion is pistonic (ideally). They do not move in the same way.

I'll try and put it into words that are clear sorry if it's too simple or I just make it more confusing!

Imagine a sine wave, a constant note. For a deep note, the driver moves a large distance, physically. Maybe it moves 5mm forward and 5mm back, total of 10mm to reproduce this wave. (this is not a headphone driver btw!). It moves back and forth at the speed of the frequency of the note, say, 30Hz, so back and forth 30 times a second.

*The number of times it moves in a second is the frequency, the distance it moves is the volume.

If the driver was given a higher sine wave, at the same volume as the low note, it may move back and forth a total of say 1mm. Maybe that's a 300Hz note.

The driver passes back and forth through it's true center (rest position) 300 times a second.

But it doesn't have to. It just has to move back and forth by 1mm at 300Hz, regardless of where the driver is in respect to it's true center. It can do this while also moving back and forth through it's actual true center at 30Hz.

Wave your hand back and forth quickly, over a distance of say 1 inch. Maybe 5 times pper second. You can keep vibrating your hand back and forth quickly whilst also moving your hand around the room, say over a distance of 6 inches, back and forth. Maybe takes 1 second. You are creating a 5Hz wave and a 1Hz wave at exactly the same time. Feel the bass!

(Just not very loudly, SPL, limited by low sensitivity of human hand in free air, is pathetic).

I hope that helps explain it!

Steve.

 

[mape00]

The driver doesn't just have to move back and forth to reproduce a simple sine. It should be able to reproduce any waveform (containing frequencies in the audible spectrum).

Containing frequencies!?, you might say. Well, there's a theorem in mathematics that (very loosely) says you can represent any waveform as a sum of sines and cosines. If I draw any waveform on a paper in the interval [-L/2,L/2], I can, in a sense, get arbitrarily close to that shape by adding terms c0 + a1*cos(2*pi*x/L) + b1*sin(2*pi*x/L) + a2*cos(4*pi*x/L) + b2*sin(4*pi*x/L) + ...

Our ears/brain somehow decomposes the audio signal (does a Fourier transformation, in mathematical terms) into these sines and cosines so that what we perceive is a linear combination (sum) of pure tones.

The fallacy of your argument is that a driver can only vibrate at one frequency at a time. This is almost true for say a tuning fork, but a driver ideally vibrates in accordance with an electrical signal, the music, which isn't a sine.

 

[myinitialsaredac]

Mmm, interesting question. I would agree with gamerphil, odigg, the predator, and mape00 as they seem to have very logical answers. It makes sense that it is only one wave being reproduced at a time because of the movement and that our brain breaks apart the complex sound into its lesser parts as mape's equation would be.

However arent there systems that have separate drivers for highs, mids, and lows. Then the crossover system on the electric side kicks in to split them. Imagine your brain doing this, but with far greater accuracy.

Dave

 

[tintin47]

Quote:

Originally Posted by mape00 /img/forum/go_quote.gif The driver doesn't just have to move back and forth to reproduce a simple sine. It should be able to reproduce any waveform (containing frequencies in the audible spectrum). Containing frequencies!?, you might say. Well, there's a theorem in mathematics that (very loosely) says you can represent any waveform as a sum of sines and cosines. If I draw any waveform on a paper in the interval [-L/2,L/2], I can, in a sense, get arbitrarily close to that shape by adding terms c0 + a1*cos(2*pi*x/L) + b1*sin(2*pi*x/L) + a2*cos(4*pi*x/L) + b2*sin(4*pi*x/L) + ... Our ears/brain somehow decomposes the audio signal (does a Fourier transformation, in mathematical terms) into these sines and cosines so that what we perceive is a linear combination (sum) of pure tones. The fallacy of your argument is that a driver can only vibrate at one frequency at a time. This is almost true for say a tuning fork, but a driver ideally vibrates in accordance with an electrical signal, the music, which isn't a sine.

I would like to add that this works because your eardrum transmits the complex waveform into your inner ear, and the sound receptors, which are basically tiny hairs, are each sensitive to a different resonant frequency. They "deconstruct" the complex waveform by hearing basically one tone each and then your brain reconstructs all of the different tone info into sound.

 

[Tridacnid]

Ever heard of a musical term called hemiola? I assume that this functions in much the same way as a driver. Here's an article on wikipedia: Hemiola - Wikipedia, the free encyclopedia

Essentially you can have two different rhythms going at the same time (for instance, triplets in your left hand and eighth notes in your right hand). This makes a complex rhythm, but you can still hear the separate rhythms going on.

 

[odigg]

Thanks for all the answers. They make sense.

I think the part that is still baking my mind is that the brain can do all this. It's just one of those "Isn't nature amazing?" types of moments.

 

[gregorio]

Odigg - A couple of things. 1st in nature there is almost no such thing as a single tone. Taking your example of the cello, it plays a single note but that note is not a single tone. It contains a fundamental tone, +1 an octave higher, +1 a fifth higher, +1 a fourth higher and so on up to about twenty different tones, these are call harmonics and the combination of them make up a note. Now, whether we hear that note as a cello note or a flute note is entirely dependant on the balance between these harmonics. It's the harmonic series and the balance of the harmonics which gives timbre and from the timbre we can tell any instrument or sound apart. So even a single note on a cello is in fact quite a complex waveform, adding a flute to the equation just makes the waveform a little more complex, it's still a single waveform it's just more complex and a speaker cone can recreate complex waveforms. Furthermore, if the speaker cone is large, it has quite a bit of mass, so producing complex high frequencies is not easy (or very accurate) because the speaker cone has to change direction very rapidly and with a big mass and inertia it's not easy to do, that's why we have tweeters which are very small, have relatively little mass and can handle the change of direction easier.

If you think the brain is clever the way it can separate sounds and instruments out of a complex waveform, that's one of the simplest things it does! Working in music production or film post-production is a real eye opener as to the lengths we sometimes have to go to in order to fool the ear.

G

 

[Tridacnid]

^ Good point. These differences in harmonics create timbre. Without subtle changes in harmonics, everything would sound the same. Now that would be boring.

 

[odigg]

gregorio - That makes a lot of sense and helps explain things. I'm still astonished by the capacity of human hearing.

 

[Fitz]

For a visual example of the complexity of seemingly simple notes, here's the waveform for D# on a bass guitar using a pick.


Immediately after sounding the note:


1 second later: