Posted: 4/17/2008 9:43:43 AM
Thomas Grillo

From: Jackson Mississippi

Joined: 8/13/2006

If anyone has any question about how heterodyning works, they need only to visit the teen buzz ringtone page where they have a collection of VHF audio tone samples.

I can hear up to about 17.4 kHz to 18 kHz, by the way, and that at 44 years of age noe less.

Anyway, on with it. Just click on any two, or more of the samples at the same time, and notice how the combination of the two VHF tones creates an audible undertone.

If that site ever goes away, I'll set up a heterodyn demo on my site. But, here's the link as it exists as of this writting.

Posted: 4/17/2008 10:01:35 AM

From: Eastleigh, Hampshire, U.K. ................................... Fred Mundell. ................................... Electronics Engineer. (Primarily Analogue) .. CV Synths 1974-1980 .. Theremin developer 2007 to present .. soon to be Developing / Trading as WaveCrafter.com . ...................................

Joined: 12/7/2007

Hi Thomas - Interesting tests! - But if you cant hear the 15kHz, be sure your audio system is actually reproducing it! - Laptops with built in mini speakers are often hopeless, and you may get nothing out above about 12kHz.. so play your PC through a good system before you worry that you are going deaf!
Posted: 4/17/2008 1:22:42 PM

From: Croxley Green, Hertfordshire, UK

Joined: 10/5/2005

An interesting test indeed. I can hear up to 14kHz distinctly, at 15 there is a marked drop in volume and above that I feel it in the back of my head rather than hear it. (I'm 46, that's the normal result, apparently.) Love that heterodyned sound btw. I spent some time on the web-page improvising. :-)

Here's another tip. Don't try this with young children or pets in the room. I can confirm that my 7 year-old hates it.

(Can you believe that these ringtones are based on ultra-sonic devices used to discourage teenagers from areas where they loiter - shops for instance. I bet people with babies [i]love[/i] that!)
Posted: 4/17/2008 3:43:09 PM

From: Escondido, CA

Joined: 2/6/2008

In junior college electronics class we gathered together all the old Heathkit sig gens, set them to "sinewave" and summed their outputs into a 'scope input to show how multiple harmonics make the waveshape start to look more and more like a squarewave.

Nowadays you could probably do this with a click or 2 on a website, but it isn't nearly as much fun.

Posted: 4/18/2008 10:15:30 AM

From: Saint Charles, MO

Joined: 4/3/2008

I'm a bit surprised to learn I can still hear the 22khz tone, at age 36. It's very subtle though and I doubt it'd work for me as a ringtone.
Posted: 4/19/2008 11:59:38 PM
Thomas Grillo

From: Jackson Mississippi

Joined: 8/13/2006

For your own frequency generator, go to:


This one works on all operating systems. It gives you 3 tone generators to work with. They go from 4 Hz on up to about 23000 Hz.

Just for kicks, I cranked up the sub woofer, and set the following frequencies:

Carrier set to 635 Hz, waveform to Sine.

Modulator 1 set to 611 Hz, set to AM, Wave= Triangle.

Modulator 2 set to 25 Hz, set to AM, Wave=Sine

All 3 amplitudes should be at maximum.

PC volume should be about 65 to 70 percent.

You should see a large interesting undulating S wave, and hear an interesting set of harmonics, with a very low frequency that pulses. It'll either feel relaxing, or annoy the daylights out of you. Try it on multiple computers.
Posted: 4/20/2008 12:34:02 AM

From: Fresno, California USA

Joined: 3/26/2006

Wow, amazing (to me) what you folks can hear! My hearing crapped out around 4,000 cps when I was in my twenties, thirty years ago. (The Army figured I couldn't hear well enough to pull a trigger; said they were afraid I might suffer further hearing loss if I were exposed to loud noises...) I think it's a little worse now, but not by much.
Posted: 4/26/2008 1:44:08 PM

From: Atlanta, Georgia

Joined: 4/24/2008

There's actually something subtle going on here which isn't quite heterodyning in the same sense as a Theremin (though it's similar).

Within the bandwidth your sound system is capable of producing (let's say, about 24 kHz), audio reproduction is ideally linear in the time domain. This means that if you play two or more pure tones simultaneously on your computer, the audio output should contain only those two frequencies without any harmonics. Of course your sound system isn't perfect and there are nonlinearities, but they are exceedingly small and mostly imperceptible for most reasonable equipment.

Visually you can see what linear reproduction means by mixing together two tones in some audio software and observing the results. Here is an example (http://i26.tinypic.com/34eqjxw.jpg). The top track is the linear combination of a 3 kHz and 4 kHz tone, and the bottom tracks are the two respective pure tones. This is a Fourier transform (http://i29.tinypic.com/eip6wh.jpg) of the top track, which shows the frequencies contained within. Notice that there are peaks at 3 and 4 kHz, but no peaks at the sum or difference frequencies. This is linear mixing and is how the audio system in your computer is supposed to work. There does exist a volume envelope at 1 kHz, which is typically called a beat frequency and could be perceived as tremolo, but this isn't truly a 1 kHz tone.

However, it is true that you can sometimes hear a difference frequency of two pure tones, even if the output of your speaker doesn't contain that frequency. What's actually at play (assuming your speakers aren't to blame*) is the non-linear response of your ear and brain, that is, your physical and neurological interpretation of sound. While there is not actually a difference frequency produced by linear mixing, for certain frequency combinations you can still hear sum and difference tones due to the way your hearing works. I've usually heard this phenomenon referred to as "combination tones", but I think I've at least once seen it called heterodyning (in general, heterodyning is any nonlinear mixing of waves, whether they be mechanical, electromagnetic, or otherwise). These kinds of psychoacoustics are heavily studied and often applied in lossy compression algorithms like MP3 in order to eliminate data which may be redundant given the way we perceive sound.

The heterodyning that occurs in a typical Theremin setup happens in an electrical nonlinear device, for example a diode or cut-off transistor or vacuum tube. These devices inherently respond non-linearly to input signals and can approximate multiplication. Therefore, at the output of the mixer circuitry in a Theremin, there exist true sum and difference tones of the RF oscillator frequencies. If this were not the case and the mixer acted linearly, the filters which remove the inaudible RF signal and would produce no audible output!

So, the effect you're experiencing with these test tones is heterodyning of a sort, but it's your ear and brain which are producing the difference notes you perceive, not your audio system! *

* Disclaimer: Non-idealities in your speakers, D/A converters, and amplifiers can indeed produce some nonlinear effects in your sound. However, these effects are usually avoided as much as possible in audio system design except where specifically desired (like in an overdriven guitar amp).

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