Is the Doppler effect really linrar?

By considering wavelengths in air and propagation times, it seems
trivial to show that (c = speed of sound in air; s = speed of source
toward the observer; o = speed of observer toward the source; f =
original frequency; f' = measured frequency at the observer) for a
stationary observer, 

         c                                      c + o
f' = f �����  and for stationary source, f' = f ����� . When both
move,        c - s                                      c
                                 c + o
we have by superposition, f' = f ����� , given in many texts. When
the                                   c - s

distance between source and observer remains constant while both move,
Numerator and denominator become equal (remember my sign convention), so
the shift becomes zero, as it must. So here's an example of division by
a variable yielding a valid superposition; it's a linear system. I don't
know why I'm sort of surprised; I've known this for a long time.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:
> By considering wavelengths in air and propagation times, it seems
> trivial to show that (c = speed of sound in air; s = speed of source
> toward the observer; o = speed of observer toward the source; f =
> original frequency; f' = measured frequency at the observer) for a
> stationary observer, 
> 
>          c                                      c + o
> f' = f �����  and for stationary source, f' = f ����� . When both
> move,        c - s                                      c
>                                  c + o
> we have by superposition, f' = f ����� , given in many texts. When
> the                                   c - s
> 
> distance between source and observer remains constant while both move,
> Numerator and denominator become equal (remember my sign convention), so
> the shift becomes zero, as it must. So here's an example of division by
> a variable yielding a valid superposition; it's a linear system. I don't
> know why I'm sort of surprised; I've known this for a long time.
> 
> Jerry

A moving source(radially wrt to a receiver) emits a frequency f1  and 
the receiver observes f1'.  The same source backs up and follows its 
prior trajectory but emits frequency f2 and the receiver observes f2'.
The receiver backs up and again follows the same trajectory but now 
emits f1 and f2 simultaneously. The receiver observes f1' and f2', the 
system is linear because the observation is a superposition of the 
component responses.  Division has nothing to do with it.

Stan Pawlukiewicz wrote:
> 
> Jerry Avins wrote:
> > By considering wavelengths in air and propagation times, it seems
> > trivial to show that (c = speed of sound in air; s = speed of source
> > toward the observer; o = speed of observer toward the source; f =
> > original frequency; f' = measured frequency at the observer) for a
> > stationary observer,
> >
> >          c                                      c + o
> > f' = f �����  and for stationary source, f' = f ����� . When both
> >        c - s                                      c
> >                                        c + o
> > move, we have by superposition, f' = f ����� , given in many texts.
> >                                        c - s
> >
> > When the distance between source and observer remains constant while 
> > both move, numerator and denominator become equal (remember my sign
> > convention), so  the shift becomes zero, as it must. So here's an
> > example of division by a variable yielding a valid superposition; 
> > it's a linear system. I don't know why I'm sort of surprised; I've > > known this for a long time.
> >
> > Jerry
> 
> A moving source(radially wrt to a receiver) emits a frequency f1  and
> the receiver observes f1'.  The same source backs up and follows its
> prior trajectory but emits frequency f2 and the receiver observes f2'.
> The receiver backs up and again follows the same trajectory but now
> emits f1 and f2 simultaneously. The receiver observes f1' and f2', the
> system is linear because the observation is a superposition of the
> component responses.  Division has nothing to do with it.

This whole subject came up because the local ice cream truck seems to be
in tune (Pachelbel's Canon!) when it approaches but out of tune as it
recedes. I had to do the math to convince myself and my son that our
ears were playing tricks.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:
> 
> This whole subject came up because the local ice cream truck seems to be
> in tune (Pachelbel's Canon!) when it approaches but out of tune as it
> recedes. I had to do the math to convince myself and my son that our
> ears were playing tricks.

Maybe the comp.dsp community needs to develop the Anti-Doppler Digital
Ice Cream Truck (ADDICT).  It would use beam forming and pitch shifting
to correct for doppler (based on the speedomter reading).  The first
prototype would assume a stationary receiver, but later models could add
radar to adjust for moving receivers.

Maybe we can get a grant from the Commerce Department.

;-)


-- 
Jim Thomas            Principal Applications Engineer  Bittware, Inc
jthomas@bittware.com  http://www.bittware.com          (703) 779-7770
Getting an inch of snow is like winning ten cents in the lottery -
Calvin

Jerry Avins wrote:
> Stan Pawlukiewicz wrote:
> 
>>Jerry Avins wrote:
(snip)
> 
> This whole subject came up because the local ice cream truck seems to be
> in tune (Pachelbel's Canon!) when it approaches but out of tune as it
> recedes. I had to do the math to convince myself and my son that our
> ears were playing tricks.
> 
> Jerry

Your ears might be fine.  I read a paper a while back published in 
Russia in underwater acoustics.  It turns out that if the medium is also 
in motion, the principal of reciprocity does not hold.

The other possibility might be a pertibation of the model frequencies of 
an observer, with and without ice cream in their belly, ;)

"Jerry Avins" <jya@ieee.org> wrote in message
news:3F43A8EF.B1F82FBD@ieee.org...

(snip about linearity and Doppler)

> This whole subject came up because the local ice cream truck seems to be
> in tune (Pachelbel's Canon!) when it approaches but out of tune as it
> recedes. I had to do the math to convince myself and my son that our
> ears were playing tricks.

In that case, I missed the whole question.

It is, to a certain extent, non-linear in v, but always linear in f.

Now, consider that the truck may be accelerating, v is not constant, and so
now it is non-linear in f.

This reminds me of a book I once read, about harmonics and music.  Many
natural sounds include harmonics of the fundamental, and our musical scale
is based on that.  So someone wondered, if instead of an octave being a
factor of 2 in frequency it was a factor of 2.1 instead, what would music
sound like?  They then created music by adding pure sine waves of the
appropriate frequencies, which of course sound horrible.   That is the
effect of non-linearity (in f) on music.

-- glen

Jim Thomas <jthomas@bittware.com> wrote in message news:<3F43B327.24B65B51@bittware.com>...
> Jerry Avins wrote:
> > 
> > This whole subject came up because the local ice cream truck seems to be
> > in tune (Pachelbel's Canon!) when it approaches but out of tune as it
> > recedes. I had to do the math to convince myself and my son that our
> > ears were playing tricks.
> 
> Maybe the comp.dsp community needs to develop the Anti-Doppler Digital
> Ice Cream Truck (ADDICT).  It would use beam forming and pitch shifting
> to correct for doppler (based on the speedomter reading).  The first
> prototype would assume a stationary receiver, but later models could add
> radar to adjust for moving receivers.

Of course... why not take advantage of the shouts (and doppler) of the kids 
running towards the truck as well... the sound of the shoes hitting the 
pavement could also be included...

Rune

On Wed, 20 Aug 2003 12:59:27 -0400, Jerry Avins <jya@ieee.org> wrote:

>Stan Pawlukiewicz wrote:

>> A moving source(radially wrt to a receiver) emits a frequency f1  and
>> the receiver observes f1'.  The same source backs up and follows its
>> prior trajectory but emits frequency f2 and the receiver observes f2'.
>> The receiver backs up and again follows the same trajectory but now
>> emits f1 and f2 simultaneously. The receiver observes f1' and f2', the
>> system is linear because the observation is a superposition of the
>> component responses.  Division has nothing to do with it.
>
>This whole subject came up because the local ice cream truck seems to be
>in tune (Pachelbel's Canon!) when it approaches but out of tune as it
>recedes. I had to do the math to convince myself and my son that our
>ears were playing tricks.
>
>Jerry

Stan made the point that I was going to make, that superposition can
be demonstrated as shown for the Doppler effect.  This does, of course
assume that the relative velocities and paths of the movers are
constant over the observation time.  Glen pointed this out as well.

Also, I think you got lucky with the Ice Cream truck.  I can't
remember how long it's been since I heard one that was remotely in
tune.  I suspect that many of them use tape loops that have made 10^n
trips through the loop and are a tad stretched, and unevenly so.
Maybe the heat here aggravates that, but the Ice Cream tunes here are
tres bizarre.

Pachelbel's Canon does seem like an odd tune for an Ice Cream vendor.
The truck in my old neighborhood used to play ragtime tunes, which I
thought was pretty cool except for the distortion.


Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

"Eric Jacobsen" <eric.jacobsen@ieee.org> wrote in message
news:3f43e793.706710706@news.west.earthlink.net...
> On Wed, 20 Aug 2003 12:59:27 -0400, Jerry Avins <jya@ieee.org> wrote:
>

> Pachelbel's Canon does seem like an odd tune for an Ice Cream vendor.
> The truck in my old neighborhood used to play ragtime tunes, which I
> thought was pretty cool except for the distortion.

The ones in Seattle play Daisy.

-- glen

"Glen Herrmannsfeldt" <gah@ugcs.caltech.edu> writes:

> "Eric Jacobsen" <eric.jacobsen@ieee.org> wrote in message
> news:3f43e793.706710706@news.west.earthlink.net...
> > On Wed, 20 Aug 2003 12:59:27 -0400, Jerry Avins <jya@ieee.org> wrote:
> >
> 
> > Pachelbel's Canon does seem like an odd tune for an Ice Cream vendor.
> > The truck in my old neighborhood used to play ragtime tunes, which I
> > thought was pretty cool except for the distortion.
> 
> The ones in Seattle play Daisy.
> 

Greensleeves here.

Ciao,

Peter K.

-- 
Peter J. Kootsookos

"Na, na na na na na na, na na na na"
- 'Hey Jude', Lennon/McCartney