When an ultrasonic motion sensor is not aligned correctly with an object's motion, the geometry of the transmitted and reflected sonar signals leads to an underestimate of velocity. This is not a large effect under most teaching laboratory conditions, but compounding such an error in the production of acceleration data can produce surprisingly large overestimates. Presented here is an analysis of the general problem for free-fall experiments, followed by experimental data that show the relative importance of these errors.

Topics
Sonar, Ultrasonics, Airplanes, Signal processing, Polymers, Interpolation, Educational aids, Educational assessment, Teaching, Laboratories
1.
Dan
 
Maclsaac
 and
Ari
 
Hämäläinen
, “
Physics and technical characteristics of ultrasonic sonar systems
,”
Phys. Teach.
 
40
,
39
–
46
(
2002
).
https://doi.org/10.1119/1.1457828
Google Scholar
Crossref
Search ADS
 
2.
A.
 
Hämäläinen
 and
D.
 
MacIsaac
, “
Using ultrasonic sonar rangers: Some practical problems and how to overcome them
,” in
Proceedings of XXXVI Annual Conference of the Finnish Physical Society
, March 14–16,
2002
.
Google Scholar
 
3.
Although traffic radar operates utilizing the Doppler effect, not echo timing, the error still applies.
4.

The experiments were done in Ft. Myers, FL, USA, at 26.4645° latitude and −81.7736° longitude. According to the U.S. Geological Survey, the local value of g should be 9.80665 m/s2 with variations no larger than 10 mGal (0.0001 m/s2).

5.
Vernier Software and Technology, LLC, “Vernier Motion Detector 2 Manual,” available online at <http://www.vernier.com/files/manuals/md-btd.pdf>.
6.

The model PASPORT Motion Sensor PS-2103A was used.

© 2015 American Association of Physics Teachers.
2015
American Association of Physics Teachers
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