audible resultant from two supersonic frequencies?

[Sarah Fox]

Hi Bob,

> >....Back to your original question, Ric. I made a recording for you, and
> >you can hear the resultant tone.  I made a wav file of 20K and 20.5K
> >tones, one in each ear.  Then I combined them into a single mono file.
If
> >you play it in good headphones and turn up the volume loud, you can just
> >hear the 500hz tone as a pitch.
>
> The process of making wav files includes time-sampling and quantization,
> both of which are somewhat non-linear.  If there is a 500 Hz resultant in
> Don's wav file, it is probably an artifact of the imperfections of the
> recording process.  If it were possible to record 20 kHz and 20.5 kHz
tones
> and mix them with no distortion at all, then there would be no 500 Hz
> resultant.  Since it is hard to find such a perfect recording system, then
> the theory can perhaps be tested by finding a poorer recording system -
one
> with more distortion.  If my theory is correct, the resultant tone should
> be even stronger when played on such a system with more distortion.

Actually the lonlinearities would have to be in the playback process, not
the recording process.   I'll point out that 20 and 20.5 kHz wav files are
somewhat suspicious, considering that those frequencies are so close to the
Nyquist rate (max sampling rate before aliasing).  It is possible that 500
Hz heterodyne products are being created as a result of sampling
peculiarities.  However mixing the signals into a mono file is a linear
process.  Distortion products from the playback would be harmonically
related -- 40 and 41 kHz, 60 and 61.5 kHz, etc.  I don't doubt the creation
of a 500 Hz signal, but I'm not sure really what is going on with this
experiment.

Playing two notes very loudly on the piano is probably a better test, since
nonlinearities are known in string behavior and since it is quite possible
for movement induced by one string to modulate the vibratory behavior of an
adjacent string -- probably with both frequency- and amplitude-modulation
components.  Very messy!  Adding to the messiness are the unisons, whose
phasing and pitch (realistically) are variable.  The experiment might be
aided by muting two of the three unisons on each note.  Of course that
decreases the RMS amplitude by almost 5 dB.

Peace,
Sarah