[sdiy] Phase shifts and instantaneous frequency

[cheater cheater]

They will cancel after LCM(1/200, 1/201) seconds.

Ian:

Scientific qualifications: have started studying maths in the
maths-phys department at 17 years old and studied since.

Why am I questioned about this?

If there's something you don't understand, ask, but please don't make
it sound like I'm making stuff up?

...

On 7/16/08, harrybissell at wowway.com <harrybissell at wowway.com> wrote:
> You said "cancellation is incomplete" ???
>
>  That implies that there is some point at which the
>  cancellation is complete. They will never cancel.
>
>  (I have not seen Tom's picture yet, so maybe I'm still
>  not understanding what you mean by cancel...)
>
>  H^) harry
>
>
>
>
>  On Tue, 15 Jul 2008 22:07:46 +0100, cheater cheater wrote
>
> > Harry,
>  > wrong,
>  > the 201 Hz partial and the 100 Hz partial start out at phase 0, but
>  > after some time they'll be exactly out of phase, at which point they
>  > cancel.
>  > Until that happens, the cancelation is incomplete and goes from
>  > minimum to maximum.
>  >
>  > The beating is 0.5 Hz because the lenght of a 200Hz wave is half of a
>  > 100 hz wave's lenght. Or, the other way around, two lenghts of the
>  > 201Hz wave are the lenght of a single 100.5 Hz wave. You should
>  > experience beating at 0.5 Hz, so of a lenght of 2 seconds, which you
>  > can clearly see on Tom's picture.
>  >
>  > What you don't experience is the fact that you should be hearing a
>  > 0.5Hz fundamental instead of 0.5Hz beat *if your ears were perfect*.
>  >
>  > Whether or not laws of physics were written down already when you
>  > were born, doesn't say that they did not exist. :P
>  >
>  > Cheers
>  > D.
>  >
>  > On 7/15/08, harrybissell at wowway.com <harrybissell at wowway.com> wrote:
>  > > Remember that Ian has assumed SINE waves of 100Hz and 201Hz.
>  > >  they will NOT beat, because there are no harmonics at all
>  > >  (so nothing to beat).
>  > >
>  > >  You need a non-linear mixer, which the ear provides.
>  > >
>  > >  There may be something of the 'missing fundamental' detection
>  > >  that human beings have.  The 100Hz and (presumed) ~almost~ second
>  > >  harmonic might give some perceptual effect.
>  > >
>  > >  I'm just trying to set this straight before Ian comes back and
>  > >  spanks you. You know that Ian was born before Physics books existed...
>  > >  at least those printed with movable type...  :^P
>  > >
>  > >  H^) harry
>  > >
>  > >
>  > >
>  > >  On Tue, 15 Jul 2008 15:00:54 +0100, cheater cheater wrote
>  > >
>  > > > No, the beats are a normal physical phenomenon. Back to physics
>  > >  > books, Ian ;)
>  > >  >
>  > >  > The original thread's question was about a constant phase
>  > >  > relationship - not a variable one. Of course you can hear a variable
>  > >  > phase relationship, which is called pitch bending. :P
>  > >  >
>  > >  > Cheers
>  > >  > D.
>  > >  >
>  > >  > On 7/15/08, Ian Fritz <ijfritz at comcast.net> 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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>  > >
>  > >
>  > >
>  > > Harry Bissell & Nora Abdullah 4eva
>  > >
>  > >
>
>
>  Harry Bissell & Nora Abdullah 4eva
>
>