[sdiy] Phase shifts and instantaneous frequency

[Tom Wiltshire]

Ian,

I did try it, and as expected I hear a repetitive throbbing in the  
resulting tone. The 1Hz effect is clearly visible in the wave;

http://www.electricdruid.com/beatwave.jpg

Since I can see a 1Hz effect in the waveform in front of me, I'm not  
entirely convinced by your explanation that this is only a non-linear  
effect of our hearing. It looks to me like my ears are picking up a  
1Hz variation which exists in this waveform.

Also, claiming that something that changes at 1Hz is "Quasi-static"  
and therefore says something about waveforms that don't change at all  
seems a bit disingenuous. No-one ever claimed an LFO isn't  
oscillating just because it goes down to 0.1Hz!

I don't understand what I'm hearing exactly, since the sum and  
difference frequencies are so far wrong, but it does seem like I'm  
hearing what I see.

Can you clarify what is going on?

Thanks,
Tom


On 15 Jul 2008, at 13:52, Ian Fritz wrote:

> You can *easily* demonstrate to yourself that differences in phase  
> are, in fact, audible.  To do this, make a signal with two sine  
> waves at 100 and 201 Hz.  This is a signal with a slowly varying  
> phase difference between the two components.  If the phase  
> differences don't matter, then you will hear a steady tone.  If  
> they do matter, then you will hear beats.  In fact, you *do* hear  
> beats.  Yes, you can easily detect phase differences between two  
> tones.  (I learned about this from one of the websites I ran across  
> during our previous discussion of this topic.)
>
> What's going on?  The beats are a result of nonlinear mixing in the  
> ear!  They do not occur at low volume levels, or if the signals are  
> presented separately to each ear.  You can easily demonstrate this  
> to yourself, also.  The nonlinear mixing produces a difference tone  
> at 101 Hz, which beats against the 100 Hz signal.
>
> Try it!
>
>   Ian
>
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