Re: [Phys-l] question on averaging.

[curtis osterhoudt <flutzpah@yahoo.com>]

Doppler sonar can be fantastically accurate (*and* precise!). In air, of course, one generally has to work with lower frequencies than in, say, water, but still, several hundreds of kHz is a common carrier frequency. For water/solids-based measurements, I routinely get into the 0.1 mm / second velocity regime (this with a homemade mixer/envelope unit); using a commercial medical Doppler unit (Parks Electronics), sub-mm /sec velocities are commonly measured. I'm sure you can get to mm/sec accuracy with some air-coupled transducers set side-by-side. 
   My homemade units consist of an analog multiplier (MLT-04s work well, and you can get them cheaply or even for free if you order samples) and then a low-pass LRC filter (Chebyshev if a strict bandwidth is needed, designed using QUCS; simply LC if a gradual roll-off is sufficient). These multipliers work just fine even without pre-amplifying the mixed signals. Let the chip do the processing for you; it's much easier than capturing raw signals and post-processing (though in my lab we've shown that it can be done in efficient software, even in real-time, with multi-MHz carriers). With good curve-fitting software (rather than a windowed Fourier-based method) a *clean* one-cycle signal is more than enough to figure out its frequency to perhaps 0.1%; several cycles will easily get you another order of magnitude precision. 
    
    One of the big advantages of the technique is that it doesn't really care about the air sound speed (within reason). The signal is generally much faster than the sound-speed changes (over laboratory length scales) and in a monostatic setup, even if there's a constant air flow, the frequency shifts due to air flow cancel each other.

   Your microwave idea is a good one, and MiniCircuits used to sell little microwave horns and the associated mixers for a low-power setup. They have the advantages that if students point them at walls, they can see movements of people on the other side of the walls; hooking up the output to an audio amp and speaker is a dramatic demonstration. 

   

 /************************************
Down with categorical imperative!
flutzpah@yahoo.com
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________________________________
From: Brian Whatcott <betwys1@sbcglobal.net>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Thursday, February 19, 2009 10:54:27 AM
Subject: Re: [Phys-l] question on averaging.

curtis osterhoudt wrote:
> With a Doppler system  :)
>
> --co
>
> ========Original message follows:============
> How does one observe the speed of a bob?
>  
Interesting proposal. If one substitutes measuring delta frequency
in place of delta position, one has several modalities from which to choose:
dopplar sonar
doppler radar and
doppler lidar.

Sonar? Supposing the bob is moving at a top speed of 0.3 m/s
then the delta f would be 0.3/342  - a  0.1% difference

But c varies appreciably with temperature: 331 to 342 m/s
over 20 degC for example
so the need for temperature control would be quite stringent.
To be confident of ones reading to 0.1 percent accuracy might
call for holding ambient temp within 
2* (342 - 331)*100 / (20 * (342 + 331)
say 0.2 percent of its nominal reading in degC -  say 30 millideg C

Perhaps doppler radar would work better?
Looking for 0.1% accuracy with a direct counting method,
might call for counting 1000  cycles at the pendulum speed of interest
during some small distance for which the bob's speed is reasonably constant,
say  0.01 m   I imagine this would be a millimeter wave doppler,
using a pendulum mounted reflector in vacuum perhaps...

Hmmm....recalling an encounter long ago with some researchers who
excited a brass instrument with a miniature spark plug in order to 
capture the
acoustic resonances, perhaps we could do as much with a fast plug discharge
in order to capture an electromagnetic echo pulse. Two shots like that
in a closely controlled time interval would certainly provide a nearly
instantaneous speed reading, one supposes.

Moving on to the supposition that measuring the positions of
multiple nodes in a resonance pipe
and averaging the adjacent measured differences of positions somehow loses
data, I have to suppose that I am misconstruing the objection.
This acoustic method is however subject to the stringent temperature
constraints already mentioned.

Written in haste

Brian W


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