Uses and Forms of Instruments: Resonator and Tuning Fork in Rayleigh's Acoustical Experiments

Summary

The resonator and the tuning fork were major instruments in acoustics in the latter half of the nineteenth-century. In particular, the third Baron Rayleigh made extensive use of these instruments throughout his long career as an experimentalist. These instruments underwent a number of alterations during their use as central experimental tools in acoustics. Functional and structural alterations were introduced in the adaptation of these instruments to several major acousticians’ experimental settings. Rayleigh not only adopted the two instruments as objects of mathematical and experimental investigation but also employed them ingeniously for various purposes. His continuing creation of a variety of uses and forms of these instruments contributed to focusing acoustics on pure tones and musical sounds until the early twentieth century.

Acknowledgements

I am grateful to Ivor Grattan-Guinness and Curtis Wilson for their valuable comments and encouragement. I would like to thank the Library and Archive at Imperial College London for supplying the sources for this research.

Notes

¹ Ja Hyon Ku, ‘J.W. Strutt, Third Baron Rayleigh, The Theory of Sound, First Edition (1877–1878)’, Landmark Writings in Western Mathematics, 1640–1940, edited by Ivor Grattan-Guinness (Amsterdam, 2005), pp. 588–99.

² Rayleigh's experiments at Cavendish Laboratory were treated in the context of the institutional history of the Laboratory in Dong-Won Kim, The Emergence of the Cavendish School: An Early History of the Cavendish Laboratory, 1871–1900, Ph. D dissertation, Harvard University, 1991, pp. 67–73; Dong-Won Kim, Leadership and Creativity: A History of the Cavendish Laboratory, 1871–1919 (Dodrecht, 2002), pp. 38–44; Simon Schaffer, ‘Late Victorian Metrology and its Instrumentation: A Manufactory of Ohms’, in Invisible Connections: Instruments, Institutions, and Science, edited by Robert Bud and Susan E. Cozzens (Belligham, 1992), pp. 23–49 (37–42).

³ R.B. Lindsay, ‘Strutt, John William, Third Baron Rayleigh’, in Dictionary of Scientific Biography, edited by Charles Coulston Gillespie (New York, 1981), vol. 13, pp. 101–5.

⁴ The only biography of Rayleigh is the one written by his son Robert John Strutt, 4th Baron Rayleigh; Robert John Strutt, 4th Baron Rayleigh, Life of John William Strutt, Third Baron Rayleigh (London, 1924). It was revised and augmented with the aid of John Howard in 1968.

⁵ R.G. Arns and B.E. Crawford, ‘Resonant Cavities in the History of Architectural Acoustics’, Technology and Culture, 36 (1995), 104–35.

⁶ Penelope M. Gouk, ‘Acoustics in the Early Royal Society 1660–1680’, Notes and Records of the Royal Society of London, 36 (February 1982), 155–75 (167).

⁷ V. Carton Maley, Jr, The Theory of Beats and Contribution Tones, 1700–1863 (New York, 1990), pp. 11–23.

⁸ Robert T. Beyer, Sounds of Our Times: Two Hundred Years of Acoustics (New York, 1999), pp. 2–4.

⁹ Ja Hyon Ku, ‘Helmholtz-eui saengrihag yeongu-eui seonggyeog-gwa cheonggag-eui gongmyeong iron’(Characteristics of Helmholtz's Physiological Research and His Theory of Resonance of Hearing) (in Korean), unpublished Master thesis for Seoul National University, 1995, pp. 46–48.

¹⁰ On Ohm's influence on Helmholtz's acoustics, see R.S. Turner, ‘The Ohm-Seebeck Dispute, Hermann von Helmholtz and the Origins of Physiological Acoustics’, The British Journal for the History of Science, 34 (1977), 1–24.

¹¹ Ku (note 9), pp. 37–38.

¹² For example, Alfred M. Mayer, ‘Researches in Acoustics’, Philosophical Magazine, 326 (1875), 352–65; Silvanus. P. Thompson, ‘On Binaural Audition’, Philosophical Magazine, 25 (1877), 274–76.

¹³ Hermann Helmholtz, On the Sensations of Tone as a Physiological Basis for the Theory of Music, trans. A. J. Ellis (New York, 1885, New York, 1954), pp. 65–69. This book was first published in Germany in 1862.

¹⁴ See Ja Hyon Ku, ‘Rayleigh-eui eumhyanghag yeongu-eui seonggyeog-gwa seonggwa’ (The Characteristics and Accomplishments of Lord Rayleigh's Acoustical Research) (in Korean), Ph.D. dissertation for Seoul National University, 2002, pp. 43–44.

¹⁵ Ku (note 9), pp. 40–54.

¹⁶ Ku (note 9), pp. 42–44.

¹⁷ In 1869, Helmholtz replaced the resonators in the ear from Corti's rods with transversal fibers of the basilar membrane in accordance with the new anatomical findings. See Ku (note 9), p. 53; Helmholtz (note 13), p. 149.

¹⁸ David A. Pantalony, ‘Analyzing Sound in the Nineteenth Century: The Koenig Sound Analyzer’, Bulletin of the Scientific Instrument Society, 68 (2001), 16–21 (16–17).

¹⁹ Alexander Graham Bell to Silvanus P. Thompson, 30 January 1880 in S.P. Thompson, S.P. Thompson Collection, No. 32, held at Library Archives and Special Collections in Imperial College London.

²⁰ ‘Tuning fork’, in The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie (London, 2001), vol. 25, pp. 885–87.

²¹ ‘Scheibler, Johann Heinrich’, in The New Grove Dctionary of Music and Musicians, edited Stanley Sadie (London, 2001), vol. 22, p. 447.

²² A.J. Ellis, ‘The History of Musical Pitch’, Journal of the Society of Arts (March, 1880), 293–404 (297).

²³ On Scheibler's tonometer, see Myles W. Jackson, Harmonious Triads: Physicists, Musicians, and Instrument Makers in Nineteenth-Century Germany (Cambridge, 2006), pp. 151–82.

²⁴ The abbreviation cps stands for cycles per second. In the nineteenth century, several units for frequency were used by acousticians. The abbreviation cps was one of them. It means the same as the modern unit Hz. The abbreviation vps (vibrations per second) was also used frequently and meant the same as cps. However, in France vps means half of Hz, that is, 870 vps = 435 Hz. This practice originated from the seconds pendulum, which was once considered the standard of length in the late eighteenth century in Paris. The seconds pendulum ticks once in going forward and once again in returning. In the case of a pendulum, this practice could be justified, but in the case of musical sounds, the symmetry of the waveform is not formed in a cycle, so it is not suitable as a unit of frequency. In this paper, cps is used extensively.

²⁵ Johann H. Scheibler, Der physikalis che und musikalische Tonmesser (Essen, 1834).

²⁶ Steven Turner, ‘Demonstrating Harmony: Some of the Many Devices Used to Produce Lissajous Curves before the Oscilloscope’, Rittenhouse, 11 (1997), 33–51 (33–34).

²⁷ Ja Hyon Ku, ‘British Acoustics and its Transformation from the 1860s to the 1910s’, Annals of Science, 63 (2006), 395–423 (409). For detailed accounts of the process for the promulgation of Diapason Normal, see Jackson (note 23), pp. 207–30; Bruce Hynes, A History of Performing Pitch: The Story of ‘A’ (Lanham, 2002), pp. 346–49.

²⁸ Ku (note 27), 414.

²⁹ Helmholtz (note 13), p. 81.

³⁰ In 1877, Herbert McLeod and George S. Clarke invented their own method of determining pitch more precisely and measured the pitches of Koenig's tuning forks with it. They judged that Koenig's forks were not far off. See Herbert McLeod to Rayleigh, Unpublished letters to Rayleigh, 3 November 1877, in Strutt, John William (1842–1919) 3rd Baron Rayleigh, General Correspondence and Notebooks at the Research Library of the USAF Research Laboratory, Hanscom AFB, Bedford, MA, USA, held on microfilm at Library Archives and Special Collections, Imperial College London; Herbert McLeod and George Sydenham Clarke, ‘On the Determination of the Rate of Vibration of Tuning-Forks’, Philosophical Ttransactions, 171 (1880), 1–18.

³¹ D.C. Miller, Anecdotal History of the Science of Sound: To the Beginning of the 20th Century (New York, 1935), p. 86.

³² Turner (note 26), 40.

³³ Miller (note 31), pp. 87–88.

³⁴ On Koenig's acoustical research and his tuning forks, see David Pantalony, ‘Rudolph Koenig's Workshop of Sound: Instruments, Theories and the Debate over Combination Tones’, Annals of Science, 62 (2005), 57–82; Thomas B. Greenslade, ‘The Acoustical Apparatus of Rudolph Koenig’, The Physics Teacher, 30 (1992), 518–24.

³⁵ Rayleigh took the course of quantitative chemical analysis from G.D. Liveing, the chemistry professor newly employed at Cambridge University in 1867. This provided Rayleigh with his only chance to learn experiments officially. R.J. Strutt (note 4), p. 38.

³⁶ R.J. Strutt (note 4), p. 45–48.

³⁷ R.J. Strutt (note 4), pp. 104, 301.

³⁸ Rayleigh, ‘Acoustical Observations II’, Philosophical Magazine, 7 (1879), 159–62 (162) [Reprinted in Rayleigh, Scientific Papers by Lord Rayleigh (New York, 1964), art. 61, vol. 1, 402–5 (405)].

³⁹ Rayleigh, ‘Interference of Sound’, Royal Institution Proceedings, 17 (1902), 1–7 [Reprinted in Scientific Papers (note 38) art. 273, vol. 5, 401–7]. Rayleigh already used the birdcall whistle in the end of the 1870s. Rayleigh, Scientific Papers (note 38) art. 61, vol. 1, 402–5.

⁴⁰ Rayleigh, ‘On a New Arrangement for Sensitive Flames’, Cambridge Philosophical Society Proceedings, 4 (1880), pp. 17–18 [Reprinted in Scientific Papers (note 38), art. 70, vol. 1, 500].

⁴¹ Rayleigh, ‘Uniformity of Rotation’, Nature 18 (1878), 111 [Reprinted in Scientific Papers (note 38), art. 56, vol. 1, 255–56].

⁴² Rayleigh, ‘On an Instrument Capable of Measuring the Intensity of Aerial Vibrations’, Philosophical Magazine, 14 (1882), 186–87 [Reprinted in Scientific Papers (note38), art. 91, vol. 2, 132–33].

⁴³ Beyer (note 8), p. 93.

⁴⁴ Ku (note 14), pp. 178–81.

⁴⁵ Rayleigh, ‘On the Crispations of Fluid Resting upon a Vibrating Support’, Philosophical Magazine, 16 (1883), 50–58 [Reprinted in Scientific Papers (note 38), art. 102, vol. 2, 212–19].

⁴⁶ Ja Hyon Ku, Rayleigh-eui eumhyanghag yeongu-eui seonggyeog-gwa seonggwa (The Characteristics and Accomplishments of Rayleigh's Acoustical Research) (in Korean) (Paju, 2008), pp. 296–301.

⁴⁷ Ja Hyon Ku, ‘Sori-eui geuneul, bansa, ganseob, hoejeol-eui geomchul-eul wihan Rayleigh-eui seongujeog silheom-e daehan yeongu’ (An Inquiry over Rayleigh's Pioneering Experiments for the Detection of Shadow, Reflection, Interference, and Diffraction of Sound) (in Korean), Journal of the Acoustical Society of Korea, 26 (2007), 55–60.

⁴⁸ Ja Hyon Ku, ‘Rayleigh-eui sori-eui banghyang jigag yeongu-e daehan gwahagsajeog gochal’ (A Historical Inquiry about Rayleigh's Research on the Perception of the Direction of Sound) (in Korean), Journal of the Acoustical Society of Korea, 21 (2005), 695–702.

⁴⁹ R.B. Lindsay, Lord Rayleigh, the Man and His Works (Oxford, 1970), pp. 152–53.

⁵⁰ Ku (note 1), p. 593.

⁵¹ Ku (note 14), p. 153–55.

⁵² R.J. Strutt (note 4), p. 50.

⁵³ John William Strutt, ‘On the Theory of Resonance’, Philosophical Transactions, 161 (1870), 77–118 (78) [Reprinted in Scientific Papers (note 38), art. 5, vol. 1, 33–75 (34)]. However, he was not the first researcher to introduce the velocity potential. The Swiss mathematician Leonhard Euler already introduced the velocity potential in the 1750s. See Ja Hyon Ku, Rayleigh-ui suryeoghag, jeongihag yeongu (Rayleigh's Research on Hydrodynamics and Electricity) (in Korean) (Paju, 2008), p. 23; Olivier Darrigol, Worlds of Flow: A History of Hydrodynamics from the Bernoullis and Prantl (Oxford, 2005), p. 24.

⁵⁴ J.W. Strutt (note 53), pp. 110–18.

⁵⁵ Helmholtz (note 13), pp. 65–69.

⁵⁶ Helmholtz (note 13), pp. 69–70.

⁵⁷ Pantalony (note 33), 17.

⁵⁸ Rayleigh (note 55), 69–70.

⁵⁹ J.W. Strutt, ‘A Remark on a Paper by Dr Sondhauss’, Philosophical Magazine, 40 (1870), 211–17 [Reprinted in Scientific Papers (note 38), art. 4, vol. 1, 26–32].

⁶⁰ Ku (note 1), Chapt. 45. The training of mathematical technique at Cambridge University during Rayleigh's undergraduate years was systematized for the Mathematical Tripos. This process and achievements were meticulously examined in Andrew Warwick, Masters of Theory: Cambridge and the Rise of Mathematical Physics (Chicago, 2003).

⁶¹ Rayleigh, The Theory of Sound, 2nd edition (London, 1894–95; New York, 1945), vol. 2, p. 188.

⁶² Rayleigh, The Theory of Sound, 2nd edition (London, 1894–95; New York, 1945), vol. 2, pp. 189–92. This was already derived in 1870.

⁶³ Rayleigh, Unpublished Notebooks, 8 January 1878 in Strutt, John William (1842–1919) 3^rd Baron Rayleigh, General Correspondence and Notebooks at the Research Library of the USAF Research Laboratory, Hanscom AFB, Bedford, MA, held on microfilm at Library Archives and Special Collections, Imperial College London.

⁶⁴ Turner (note 26).

⁶⁵ Rayleigh, ‘Uniformity of Rotation’, Nature, 18 (1878), 111 [Reprinted in Scientific Papers (note 38), art. 56, vol. 1, 355–56].

⁶⁶ Although a similar device was invented by Danish inventor Poul La Cour in 1875, Rayleigh invented it independently. For the working mechanism of La Cour's phonic wheel, see H.M. Dadourian, ‘Characteristics of Electrically Operated Tuning Forks’, Physical Review, 13 (1919), 337–59.

⁶⁷ Rayleigh (note 63), 17 December 1879.

⁶⁸ Rayleigh (note 63), 17 September 1876.

⁶⁹ Rayleigh (note 63), 24 September 1876.

⁷⁰ Ja Hyon Ku, ‘Rayleigh-eui sori-eui banghyang jigag yeongu-e daehan gwahagsajeog gochal’(A Historical Inquiry about Rayleigh's Research on the Perception of the Direction of Sound) (in Korean) Journal of Acoustical Society of Korea, 21 (2002), 695–702 (696–97).

⁷¹ Rayleigh (note 63). From 12 July to 7 November 1904, Rayleigh performed intensive experiments on this topic for more than 38 days.

⁷² Rayleigh, ‘Acoustical Observations I’, Philosophical Magazine, 3 (1877), 456–64 (459) [Reprinted in Scientific Papers (note 38), art. 46, vol. 1, 314–21 (317)].

⁷³ Silvanus P. Thompson, ‘Note on a Mode of Maintaining Tuning Forks by Electricity’, Philosophical Magazine, 22 (1886), 216–17; W.G. Gregory, ‘On a Method of Driving Tuning-Forks Electrically’, Philosophical Magazine, 28 (1889), 490–92.

⁷⁴ In 1874, Rayleigh found that the resonator absorbed sound, but the effect was easily reversed with a slight untuning. In this experiment, the resonator was an absorber of the sound that had the components whose pitch was identical to the proper frequency of the resonator. Rayleigh (note 63), 12 February 1874.

⁷⁵ Rayleigh, ‘Acoustical Observations II’, Philosophical Magazine, 7 (1879), 149–62 (149) [Reprinted in Scientific Papers (note 38), art. 61, vol. 1, 402–5 (402)].

⁷⁶ Rayleigh (note 63), 9, 16 October 1876.

⁷⁷ Bruno Latour, Science in Action: How to Follow Scientists and Engineers through Society (Cambridge, 1987), pp. 1–17.

⁷⁸ Rayleigh (note 63), 16 October 1876.

⁷⁹ Rayleigh (note 72), 318.

⁸⁰ John Tyndall, On Sound (London, 1867, New York, 1969), pp. 179–80.

⁸¹ John Tyndall, On Sound (London, 1867, New York, 1969), p. 317.

⁸² Rayleigh, ‘On Bells’, Philosophical Magazine, 29 (1890), 1–17.

⁸³ c′ is at the middle of the keyboard of the piano. c′′ means the octave of c′ and c′′′ the octave of c′′. It follows the notation of pitches used at that time. This notation was widely used in Germany, which A.J. Ellis, the translator of Helmholtz's Tomempfindungen, introduced to Britain. See Helmholtz (note 13), pp. 15–16. According to modern notation, c′ falls on C(4).

⁸⁴ Rayleigh (note 63), 20 October 1876.

⁸⁵ Beyer (note 8), p. 15.

⁸⁶ Rayleigh (note 63), 8 March 1878.

⁸⁷ Rayleigh (note 63), 15 July 1878.

⁸⁸ Rayleigh, ‘Acoustical Observations IV’, Philosophical Magazine, 13 (1882), 340–47.

⁸⁹ Rayleigh (note 63), 13 September and 5, 14, 17 October 1878.

⁹⁰ Rayleigh, ‘Acoustical Observations V’, Philosophical Magazine, 17 (1884), 188–94 [Reprinted in Scientific Papers (note 38), art. 110, vol. 2, 268–75].

⁹¹ Rayleigh (note 63), 4, 5 December 1879.

⁹² Rayleigh (note 63), 24 December 1879.

⁹³ Pantalony (note 18), 17.

⁹⁴ Rayleigh, ‘Acoustical Notes VII’, Philosophical Magazine, 13 (1907), 318–20 [Reprinted in Scientific Papers (note 38), art. 320, vol. 5, 366–68].

⁹⁵ Interestingly, Rayleigh did not use a tonometer but a harmonium in this situation in order to measure the pitch of the tone. Although he seemed to have no reliable tonometer, he seemed to have tuned the harmonium exactly.

⁹⁶ Crosbie Smith and M. Norton Wise, Energy and Empire: A Biographical Study of Lord Kelvin (Cambridge, 1989), pp. 360–74.

⁹⁷ Ku (note 27), 421–23.