Callaway, Thomas O.

Dennis, James C.

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Stephen F. Austin State University SFA ScholarWorks Faculty Publications Physics and Astronomy 1994 Listening to Free Fall with the MacRecorder Thomas O. Callaway James C. Dennis Follow this and additional works at: https://scholarworks.sfasu.edu/physicsandastronomy_facultypubs  Part of the Physics Commons Tell us how this article helped you. The Physics Teacher 32, 88 (1994); https://doi.org/10.1119/1.2343912 32, 88© 1994 American Association of Physics Teachers.Listening to free fall with theMacRecorderCite as: The Physics Teacher 32, 88 (1994); https://doi.org/10.1119/1.2343912Published Online: 03 September 1998Tom Callaway, and James DennisARTICLES YOU MAY BE INTERESTED INThe Color of the Sun – Perception and Spectral DensityThe Physics Teacher 56, 600 (2018); https://doi.org/10.1119/1.5080572Archimedes’ Principle Using Energy ConsiderationsThe Physics Teacher 56, 616 (2018); https://doi.org/10.1119/1.5080579Driven Pendulum: An Advanced ExperimentThe Physics Teacher 56, 636 (2018); https://doi.org/10.1119/1.5080586View Online Export Citation --;-;' • - r ....,-.-:4::""=--1,~ ., Listening to Free Fall \Vith the MacRecorder Tom Callaway and James Dennis Physics Department, Stephen F. Austin State University, Nacogdoches, TX 75962 Here is a method of analyzing a classic free-fall demonstra-tion 1 using current desktop computer technology.2 You will need string, lead fishing weights from a local hardware store, a Macintosh computer, and a MacRecorder, or a comparable audio digitizer for the Macintosh. The MacRecorder digitizes eight bits of sound at a maximum rate of 22 kHz, and can play back recorded sounds, show Fig. 1. MacRecording of a string of weights hitting the floor. The weights are spaced at sounds graphically, and analyze them in 0.304-m (1-ft) intervals. several modes. For the recordings shown here, time intervals were taken directly from the sound "pictures," which are similar to digital oscilloscope frames. SoundEdit, a software package that comes with the MacRecorder, pro-vides movable markers and time bases to use with digitized frames. The lead weights are grooved so that they can be pinched onto the string. If the weights are equally spaced, then the distance from the floor for each weight is nd, where d is the spacing and n is an integer. The free-fall equation with no air resistance and zero initial velocity is nd = gt2 /2, which can be expressed as t = ✓2ndlg (1) where d is chosen to allow a reasonable time between collisions with the floor. Parameter t is the time taken for the weights to hit the floor, and nd is the total distance from the floor to each weight, with the spacing between weights equal to d and n = 1,2,3 .... u, ... Cl) .., Cl) :c C .... ... Cl Cl -~ Cl) > Cl .Cl «:I u, .., .&:. en .... Cl) 3 .... Cl ' ..,u, .... Q 3.0 2.4 1.8 1.2 0.6 0 0.2 Exper-iment81 Theor-etic81 --a--0.3 0.4 0.5 0.6 0.7 0.8 Time The difference in the time intervals between each weight collision de- Fig. 2. Experimental vs predicted times of fall for equally spaced weights (from Fig. 1). 88 THE PHYSICS TEACHER VOL. 32, FEB. 1994 ''Listening to Free i:;:au wjth the MacRecorder'' creases as the weight distance from the floor increases. This happens because each weight travels the final distance interval at a greater average speed. Thus the collisions with the floor increase in frequency as the string of lead weights falls. In Fig. 1 we see that the time inter-vals between strikes on the floor de-crease steadily when a string of equally spaced weights is dropped. In Fig. 2 we see experimental data that is in very close agreement with theory. We can conclude that the weights fall essentially freely and en-counter very little air resistance. The experimental value of g from Fig. 2 is 9.5 m2, producing a discrepancy of about 3 percent. What happens when the beads are spaced according to the free-fall equa-tion? The free-fall equation can be writ-ten as Parameter t0 is the time interval chosen to be a constant, and n is an integer index for the interval. Figure 3 is a recording offive falling weights spaced to hit at 1/s-s time intervals. It is important that the first weight be spaced at the exact calculated distance above the floor before drop-ping the string (or the first weight can ~~~~~.1~..!m~:- l.: 1ound3o:.~S!l!~~-<m~~~mf~~ ~~~®fl~~ ~ ' ~~3 p~: i' u ',>:•:1d~'!'i1 1'd ·~·•,l.j.lljt Mono lit c=Irn•I 0041 0 04 1 22t( f-.JC-iCUI] c:,j 0001 0001 Fig. 3. MacRecording of a string of weights spaced to hit the floor at 1/a-s time Intervals. be placed barely touching the floor), so as a precaution we taped the bottom of the string to the floor. The time intervals in Fig. 3 are all very nearly equal, as expected. An analysis of these recordings gives times between collisions of 1/s s ±2 percent. The error is probably due to air friction acting on the longer string needed for equally spaced collisions. Conclusion We find the MacRecorder to be an effective tool for recording and analyz-ing audible events. The MacRecorder (or any other sound digitizing device such as the Sound Impact Pro) and the built-in microphone that comes with the new Macintosh, along with the software available for analysis of sounds, in-creases our ability to perfonn a variety of novel physics experiments. For example, as one variation in this free-fall experiment we substituted a much heavier weight for one of the equally spaced small weights. The heavy weight behaved as if it were a small weight, just as Galileo had pre-dicted. This result generated some ex-citement among our students, since most of them had predicted that the heavier weight would pull down the lighter ones. Until they encountered this exercise, our students had given little thought to Galileo's fabled comparison of falling weights. This apparatus made it simple to bring history and science together. References 1. R.D. Edge, "Dropping a string of mar-bles," Phys. Teach. 16, 233 ( 1978). 2. R. Beichner, "Using Macintosh comput-ers in physics labs," Phys. Teach. 27, 348 (1989). Reveal the Cosmic Rays in Your Classroom! Our diffusion cloud chambers are large enough to provide an abundance of tracks from natural background radiation, for an enthralling view of the subatomic world. High energy cosmic rays can be watched by many students simultaneously In our 61 cm jumbo model or our 26 cm standard model. Fiducial marks enable alpha particle energy measurement. An optional magnet assembly will bend Compton scattered electron trajectory. Action of the electric force on Ions can also be demonstrated. Mechanical refrigeration is available for museum settings. "Listening to Free Fall with the MacRecorder'' An effective physics demonstration reduces the amount of information a student must accept on faith; the cloud chamber accomplishes this in an area of study usually far removed from human experience. Write, call, or FAX for details. Supersaturated Environments A Division of Reflection Imaging, Inc. P.O. Box 55252 Madison. WI 53705 PH (608) 238-5068 FAX 231-2312 VOL. 32, FEB. 1994 THE PHYSICS TEACHER 89 

Listening to Free Fall with the MacRecorder

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Listening to Free Fall with the MacRecorder

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