[sdiy] ot: rotating speaker simulation or stupid approach

[Ian Fritz]

At 02:56 AM 7/7/2003, Richard Wentk wrote:

>>I would look at this differently.  :-)
>>
>>Suppose you have two sticks to dip in the water and an observer in line 
>>with them. Now do two experiments:
>>
>>1.)  Dip the first stick twice with a time separation dt.  The two pulses 
>>will reach the observer
>>spaced by a time interval dt.
>>
>>2.) Dip the first stick and then the second, again with a time separation 
>>dt.  The two pulses will now reach the observer spaced by a time interval 
>>that is different from dt -- larger or smaller depending on which side 
>>side of the sticks the observer is located.
>>
>>This is a simple and obvious Doppler shift.
>
>No it's not. You're confusing an impulse with a continous sequence of 
>wavefronts.

Sorry, but you seem to be the one who is confused.  We are assuming a line 
of speakers (or delays) whose spacing is less that wavelength of sound 
(long wavelength limit).  Any wave can be decomposed into a series of 
impulses.  This is elementary response theory (Green's functions, 
etc.).  If successive impulses are sent to successive speakers, then a 
Doppler shift will occur, as I showed in my simplified example of two 
impulses from two sources.

>You can't Doppler shift an impulse because it has an infinite frequency 
>response to start with.

Nonsense!  You just change the effective wave velocity of each Fourier 
component and you will get a Doppler shift.  If you need to look at it that 
way.  For a more general view, you need to understand that any wave can be 
written in the form y = f(x - ct), where c is the sound velocity.  Changing 
c by motion of the source, either actual or effective, will produce a 
Doppler shift.

>A more accurate representation would be to replace each single dip with a 
>vibrator (no, not that sort... - actually thinking about it, they'd work 
>as well as anything :-) ) producing a continuous stream of wavefronts by 
>dipping up and down. Or indeed vibrating.

When the wavelength becomes comparable to the speaker (or delay) 
separation, then what you say is correct.  Several people have already 
tried to explain this to you.  This is where aliasing (or equivalently, 
interference) effects will come into play.

   Ian