This paper continues the collection of experiments that describe the use of cell phones as experimental tools in physics classroom education.1–4 We describe a computer-aided determination of the free-fall acceleration g using the acoustical Doppler effect. The Doppler shift is a function of the speed of the source. Since a free-falling objects speed is changing linearly with time, the Doppler shift is also changing with time. It is possible to measure this shift using software that is both easy to use and readily available. Students will use the time-dependency of the Doppler shift to experimentally determine the acceleration due to gravity by using a cell phone as a freely falling object emitting a sound with constant frequency.
REFERENCES
1.
E. G.
Falcão
Jr., R. A.
Gomes
, J. M.
Pereira
, L. F. S.
Coelho
, and A. C. F.
Santos
, “Cellular phones helping to get a clearer picture of kinematics
,” Phys. Teach.
47
, 167
–168
(March 2009
).2.
C.
Villa
, “Bell-jar demonstration using cell phones
,” Phys. Teach.
47
, 59
(Jan. 2009
).3.
Dave Van
Domelen
, “Teaching light polarization with cell phones
,” Phys. Teach.
45
, 469
(Nov. 2007
).4.
E. C.
Hammond
and Meron
Assefa
, “Cell phones in the classroom
,” Phys. Teach.
45
, 312
(May 2007
).5.
The Doppler shift is given by (f is the detected frequency; is the sending frequency; v is the velocity of the source; c is the speed of sound). By using the binomial approximation , the Doppler shift can be approximated to because v ≪ c for a free-falling object starting at 2 m above the ground (the upper algebraic sign is used when moving toward the observer, the lower sign when the transmitter moves away from the observer). For the source moving toward the receiver, the relation becomes
6.
Audacity (freeware for sound recording, generating, and analysis)
; see audacity.sourceforge.net.7.
Test Tone Generator (shareware stereo-sound generator)
; see www.esseraudio.com/.8.
SPEAR
(freeware for dynamic spectral analysis), see www. klingbeil.com/spear/.© 2011 American Association of Physics Teachers.
2011
American Association of Physics Teachers
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