Understanding Ultrasonic Heterodyning: EM Voltages and Human Hearing Explained

[beatfrequency]

Please help me understand what is wrong with my thinking. I have two high frequency sources into an oscilloscope with one source a few hertz difference. I have a spectrum analyzer and expected a low frequency signal due to the beat frequency of the sources. What is going wrong? I'm confused.

This is from EM voltages.

But I have a related question. Why can the human ear hear audio ranges from two ultrasonic heterodyned sources? Isn't that just a beat frequency in the audio range. Why do I not see the same principle on my spectrum analyzer? Do the ear create some kind of diode effect?

 

[rude man]

This is a very good question. Some time ago a writer wrote a paper in IEEE Spectrum confusing addition with mixing. I pointed the error out but this guy stuck to his guns. It was quite an amusing exchange of published letters.

What you did by applying the two signals to the spectrum analyzer was to add two signals: cos(w₁t) + cos(w₂t). There are no sum & difference frequencies produced by this process. There is just w₁ and w₂.

A mixing process on the other hand is essentially multiplicative: cos(w₁t)*cos(w₂t) which by simple trig gives you a signal at (w₁ + w₂) and another at (w₁ - w₂). Mixers usually are not simple multipliers so you also get other output frequencies but you will always get the sum & difference frequencies. All mixing is based on a nonlinear process. Addition is of course linear.

The human ear may have some nonlinearity which would yield a small difference frequency, like the "diode" effect you suggested. I believe on a healthy ear it's extremely small.

Two tuning forks detuned a few Hz from each other, i.e. (w₁-w₂)/2π give a sound that sounds lile a low-frequency signal but it's just the average of the two frequencies varying in intensity at the difference frequency. You obviously could not hear the beats from two tuning forks separated by a few Hz if your ear produced only a mixing operation (you might hear the sum but not the "beat" frequency.)

The beat signal for cos(w₁t) + cos(w₂t) = 2{cos[(w₂ - w₁)/2 t]}cos[(w₁ + w₂)/2 t].

This may look like new frequencies at w₁ + w₂ and w₁ - w₂ are produced, but by looking at the LHS of the equation there obvioulsy aren't. You can see though that it can be interpreted as a signal at w = (w₁ + w₂)/2 moduated in amplitude by a signal at the beat frequency (w₁ - w₂)/2.

The standard superhet radio on the other hand mixes the incoming signal (RF) with a local oscillator (LO) to produce a difference frequency called the intermediate frequency (IF).

 

[beatfrequency]

Thanks for the excellent reply.

I have another tough question. I saw a demonstration that I cannot explain how it was accomplished. Maybe someone has an idea.

I saw a compass with nothing around it for 20 or more feet. The compass needle oscillated between magnetic north and 90 degrees from its resting state, magnetic north, at about 1/3 of a hertz indefinitely but another compass 10 feet away did not.

ELF waves are not directional so I thought somehow higher frequencies which are directional could be heterdyned into a localized magnetic field to make a directional ELF EM spotlight per say.

The scientist or magician claimed he could do this on a much larger scale and turn the Earth into an NMR and ESR machine under its own magnetic field but this device helped with the signal to noise ratio. He did not explain how he projected directional ELF waves at a distance.

Any ideas?

 

[beatfrequency]

And I don't think you can use beam forming with ELF waves either.

 

[rude man]

If the 1st compass oscillated "forever" then an external mag field must have been set up somehow. The 2nd compass may have had enough static friction to not repond to that field. In which case the field would not have to have been 'beamed' at the 1st compass.

I'm sure there are several other possible explanations.