[sdiy] Phase shifts and instantaneous frequency

[cheater cheater]

Guys,

there's a lot of pseudo-science going on here.

1. 'Beats become more noticable at high volume levels'
... that's obvious.

2. 'Beats become unnoticable at low volume levels'
That's because they're much more noticable at high levels, for the
simple fact that your amp distorts more at high levels, creating all
those nice easily-noticable sidebands.

3. 'Beats correspond to combination tones'
Nope.
Combination tones happen only at audible frequencies. Not at 0.5Hz.

4. 'Helmholtz says amplitude modulation is not an effect of beats'
obviously wrong. Nobody actually said this yet, but I'm anticipating
the worst 8^)

5. 'the ear does a linear Fourier analysis'
No... just no...

No.

Makes no sense.

6. 'the power spectrum is constant in time'
Imagine you have a merry-go-round rotating at 1 RPM. there's someone
running in the opposite direction at, from his perspective, 1.1 RPM.
You're standing far away and looking.

Is the 'power spectrum' the same? It might be in an infinite analysis.
But not in a short-window analysis. Even then, this consideration is
fallacious in its own, because our ears react to the power, not to the
power spectrum, which is very, very, different. And no, our ears don't
do Fourier analysis.
What our ears react to, when searching for the pitch, is the immediate
slope at its maximum. So, to word things differently: they're reacting
to the extrema of the derivative of our signal. This is where
combination tones come from.

These combination tones, however, have nothing to do with the fact
that two oscillators that are momentarily out of phase will cancel.
Whether globally the waveform is a sine, triangle, or noise, has a
frequency of 1, 101, or 1001Hz, it will always be that 1-1 = 0.
The fact that both waves are the same waveform and almost the same
pitch (modulo multiples) means that they will 'locally' seem like two
copies the same wave, at the same pitch, just out of phase.
What then happens is that 'locally' this 'perceived phase difference'
changes, so the waves naturally vary from being 'twice the same thing'
and amplifying or being negatives of eachother and cancelling
eachother out.

See how I never mentioned volume, eardrums, or Area51 in my
explanation of the phenomenon? Yeah. Smokin'.

D.

On 7/16/08, Ian Fritz <ijfritz at comcast.net> wrote:
> At 06:02 PM 7/15/2008, Aaron Lanterman wrote:
>
>
> >
> > > The 1 Hz modulation comes from beating of the 101 Hz and 100 Hz
> > > signals.
> > >
> >
> > That might be the case, but the perceived beat seems to be more easily
> > explained by simply noting it's a wave that's periodic with a period
> > of 1 Hz.
> >
>
>  Again, the power spectrum is constant in time.  So doesn't linear signal
> theory say you would not hear beats?  That's the first-order picture, that
> the ear does a linear Fourier analysis.  And if you listen at a low volume
> level you don't hear the beats, whereas they are very pronounces at high
> volume levels.  How do you explain that with a linear theory?  *Any* linear
> theory?
>
>  And if you present the signals separately to the two ears you don't hear
> the beats, either.
>
>
>
> > There might be weird complicated intermodulations going on in
> > the ear, but we don't _have_ to fully resort to them to explain what's
> > happening in that particular example.
> >
>
>  I think you do, sorry.  :-)
>
>
>   Ian
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