Re: Dopler effect

["Ari Hamalainen" <aohamala@penger.helsinki.fi>]

> Suppose the VERNIER microphone connected to ULI is used to intercept
> sound from a 256 Hz tuning fork and the spectral line of one frequency
> is observed on the screen (zoomed ?). Then you move the microphone back
> and forth rapidly. Will the line broadening be observable?
>
> Just an idea, I never tried this. The maximum acceleration that the
> microphone (and your hand) can tolerate will limit the maximum speed,
> probably to no more than 1% of the speed of sound, I suppose.


The difficulty of this kind of experiment rises from the process that is
used to calculate the spectrum of the sound, that is, the discrete Fourie=
r
transform. The resolution of the spectrum is the inverse of the sample
length. If you have for example 0.2 second sample, then you get only 5 Hz
resolution for the spectrum. For ULI DOS software the resolution is often
even worse (I have not tried it with the new Logger Pro, though).

Me and our students have tried several times the experiment that Ludwig
proposes, both by moving a tuning fork or a  piezoelectric buzzer by hand=
,
or by putting the sound source on a cart and pushing it fast. The results
have been that the frequency shift to the right direction can be seen, bu=
t
the proportionality of the shift and the velocity can not be verified.

Quite recently, I finally managed to make a Doppler shift experiment that
gives reasonably good quantitative results too. I attached a piezo buzzer
(4.5 kHz, VERY loud end irritating) to the end of the vertical rotating b=
ar
of a Pasco Rotating Platform (#ME-8951). I rotated the system with a smal=
l
DC motor at speeds up to 10 rev/s. The anqular velocity was measured with=
 a
photogate. I used a Vernier microphone and a ULI// interface, at 10 000 S=
/s
sampling rate, and at maximum sample length, 0.74 s. By measuring the
widening of the frequency peaks, I was able to show quite plausibly that =
Df
~ v. I used my own software for data analysis, but I can't see why it wou=
ld
not be possible with standard ULI programs too.

One might be also be interested in these:

* Briotta, D. et al. The appropriate use of microcomputers in undergradua=
te
physics labs. Am. J. Phys. 55 (10), October 1987. 891=97897. The authors =
have
had nice results for the Doppler effect with an ultrasound system.
Unfortunately, they give very little details about the hardware and
software.

* Wisman, R. et al. Experimental data frequency measurement with a PC. Am.
J. Phys. 58 (6). June 1992. 570=97571. Describes a self-made measurement
system, and how Doppler experiments might be done with it, but gives no
example data.
--

Ari.Hamalainen@Helsinki.FI
Univ. of Helsinki, Department of Physics
tel +358-9-1918311 (desk), +358-40-5143867 (mobile), fax +358-9-1918680
http://www.helsinki.fi/~aohamala/