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Computer Bulletin Board
Steven D. Gammon
Calibrating Frequency Data Collection Systems Using Shortwave Radio Signals
University of Idaho Moscow, ID 83844
Ron Estler Department of Chemistry, Fort Lewis College, Durango, CO 81301;
[email protected] In many physical chemistry laboratory experiments, the measurement of a molecular observable of a particular “unknown” chemical sample is determined by standardizing the measurement against the known properties of an accepted chemical sample “standard”. More direct measurement of physical parameters using calibrated laboratory equipment is less frequent owing to the difficulty in maintaining and certifying such calibrations. With the increasing availability of computer data acquisition and manipulation in the instructional environment, such equipment calibration can itself represent a valuable student exercise. We describe here a relatively simple method of calibrating computer-based audio frequency measurements using fast Fourier transform (FFT) techniques and the nationally maintained WWV broadcasts. As FFT instrumentation has become more readily available in the primarily undergraduate institutions, teaching the basics of the Fourier transform technique has become a challenge in this undergraduate environment. Many articles in this Journal have addressed this curricular issue, including articles concerning the myriad general FFT uses in chemistry (1–5); others have addressed particular applications, such as FT–NMR (6–10); and still others show how several software packages can be used to aid FFT instruction (11–13).
Sound recording using a desktop computer has become routine. Often the user is offered several digitizing options including digitizing rate—for example, 22 kHz. This rate may be derived from an internal computer clock or from a clock on an external recording device. Regardless of the timing method, by recording readily available accurate audio signals and Fourier-transforming these files, the digitizing frequency can be calibrated for use in such an experiment as described above.
Laboratory Example One physical chemistry experiment that has benefited from this curricular effort is the determination of the heat capacity ratio of gases (γ = CP/CV) by accurately measuring the speed of sound in a spherical resonant cavity (14 ) or in a Kundt’s tube (15). Traditionally, a continuous-wave (cw) audio source and microphone are used to record those frequencies that form standing-wave patterns within the cavity. The use of FFT techniques simplifies and speeds the data collection by replacing the cw audio source with a white-noise generator. A few seconds of amplitude–time data readily transform into the required amplitude–frequency data domain. Argon has typically been used to calibrate the physical characteristics of the resonant cavity, thereby eliminating the need to accurately calibrate the sound-frequency data collection. Alternatively, accurate frequency calibration coupled with accurate physical measurements of the resonant cavity can replace standardization against a chemical standard. The question then becomes how to calibrate the frequency data collection instruments. Although it is impossible here to address all possible computer hardware and software configurations, we give one example that provides some general guidelines that can be easily adapted to any particular situation.
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Figure 1. Panel a displays an approximately 3-s record of the audio tones from WWV. This signal was recorded at a nominal softwarechosen digitizing rate of 22 kHz: 65536 (216) data points total. Panels b and c are expansions of this record at the indicated times displaying the 1000- and 600-Hz tones. The modulation of signal in panel b results from the presence of multiple frequencies at this point in the transmission. The corresponding frequency magnitude spectrum is shown in panel d with expansions in panels e and f. Panels d, e, and f represent the calibrated transformed spectra; that is, the digitizing rate has been adjusted to produce the best match to the 1000- and 600-Hz tones.
Journal of Chemical Education • Vol. 77 No. 9 September 2000 • JChemEd.chem.wisc.edu
Information • Textbooks • Media • Resources
Calibration and NIST The National Institute of Standards and Technology (NIST) operates two high-frequency (shortwave) radio stations, WWV (Fort Collins, CO) and WWVH (Kauai, HI). Both stations broadcast continuous time and frequency signals on 2.5, 5.0, 10, and 15 MHz. WWV and WWVH are referenced to the primary atomic time frequency standards maintained by NIST in Boulder, Colorado. The frequencies as transmitted are accurate to about one part in 100 billion (1 × 1011). However, the usable received accuracy is only about one part in 10 million (1 × 107), owing to various propagation effects. The audio tones that accompany these broadcasts are described in detail on NIST’s Web site (http://www.bldrdoc.gov/timefreq/ wwv/wwv.html ) and are derived from these atomic standards. They provide a convenient primary source of accurate audio frequencies for calibration. For example, Figure 1a displays approximately 3 seconds of the accompanying audio tones as received from WWV at 5 MHz on an inexpensive shortwave receiver. This signal was recorded on an older model Macintosh SE/30 (internal clock speed of 16 MHz) using a MacRecorder (a microphone hardware peripheral) at a software-chosen digitizing rate of 22 kHz, yielding 65536 (216) data points total. Figures 1b and 1c are expansions of this record at the indicated times, displaying the nominal 1000- and 600-Hz tones present. Fouriertransforming these signals produces the corresponding frequency magnitude spectrum shown in Figure 1d, with expansions in 1e and 1f. These transforms were performed using Igor,1 a powerful data analysis software application available for both the Macintosh and Windows operating systems. The integerbased files generated by the MacRecorder are opened directly by Igor, trimmed to the appropriate (2n) number of data points, and transformed using FFT macros provided within the software. Windowing (apodizing) the data is also easily explored within Igor, but was not used for the data presented here. Figures 1d–1f represent the calibrated transformed spectra. The original transformation, assuming a 22.0000-kHz sampling rate, did not produce the 600- and 1000-Hz frequency signals present in the broadcast; they were observed at frequencies 1.4% lower. To accurately reproduce these tone standards as shown, the apparent time base of the digitization was adjusted (before transformation) until a match was achieved. For this hardware configuration the calibrated digitization rate is on the order of 22.3127 kHz. Once determined, this digitizing
rate is used to accurately determine any frequency within the audio range. The precision of this method of course depends on acquisition parameters of the data collection (e.g., digital resolution) as well as the numeric precision used in the software application performing the FFT. However, this method can be applied to virtually any hardware–software configuration that allows adjustment of the apparent time scale (digitizing rate) of the recorded audio file. While standardization against an accepted chemical standard may appear more straightforward for the experiment discussed above, students should always be presented alternatives for their critical evaluation of experiments and the errors associated with various approaches. In addition, the alternative approach presented here introduces students to the supportive role NIST plays in the scientific community. Note 1. Igor is a product of WaveMetrics, Inc., P.O. Box 2088, Lake Oswego, OR 97035.
Literature Cited 1. Eastman, M. P.; Kostal, G.; Mayhew, T. J. Chem. Educ. 1986, 63, 453–455. 2. Glasser, L. J. Chem. Educ. 1987, 64, A228, A230–A233. 3. Glasser, L. J. Chem. Educ. 1987, 64, A260, A262–A266. 4. Glasser, L. J. Chem. Educ. 1987, 64, A306, A308–A313. 5. Marshall, A. G.; Comisarow, M. B. J. Chem. Educ. 1975, 52, 638–641. 6. King, R. W.; Williams, K. R. J. Chem. Educ. 1989, 66, A213–A219. 7. King, R. W.; Williams, K. R. J. Chem. Educ. 1989, 66, A243–A248. 8. King, R. W.; Williams, K. R. J. Chem. Educ. 1990, 67, A100–A105. 9. Williams, K. R.; King, R. W. J. Chem. Educ. 1990, 67, A93–A99. 10. Williams, K. R.; King, R. W. J. Chem. Educ. 1990, 67, A125–A137. 11. Zielinski, T. J. J. Chem. Educ. 1999, 76, 285–286. 12. Estler, R. C. J. Chem. Educ. 1991, 68, A220–A227. 13. Bell, H. M. J. Chem. Educ. 1993, 70, 996–997. 14. Colgate, S. O.; Williams, K. R.; Reed, K.; Hart, C. A. J. Chem. Educ. 1987, 64, 553–556. 15. Steel, C.; Joy, T.; Clune, T. J. Chem. Educ. 1990, 67, 883–887.
JChemEd.chem.wisc.edu • Vol. 77 No. 9 September 2000 • Journal of Chemical Education
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