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 The Tuning Fork:
An Amazing Acoustics Apparatus
Daniel A. Russell
   It seems like such a simple device: a U-shaped piece of metal with a stem to hold it; a simple mechanical object that, when struck lightly, produces a single-frequency pure tone. And yet, this simple appearance is deceptive because a tuning fork exhibits several complicated vibroacoustic phenomena. A tuning fork vibrates with several symmetrical and asym- metrical flexural bending modes; it exhibits the nonlinear phenomenon of integer harmonics for large-amplitude displacements; and the stem oscillates at the octave of the fundamental frequency of the tines even though the tines have no octave component. A tuning fork radiates sound as a linear quadrupole source, with a distinct transition from a complicated near-field to a simpler far-field radiation pat- tern. This transition from near field to far field can be seen in the directivity patterns, time-averaged vector intensity, and the phase relationship between pressure and particle velocity. This article explores some of the amazing acoustics that this simple device can perform.
A Brief History of the Tuning Fork
The tuning fork was invented in 1711 by John Shore, the principal trumpeter for the royal court of England and a favorite of George Frederick Handel. Indeed, Handel wrote many of his more famous trumpet parts for Shore (Feldmann, 1997a). Unfortunately, Shore split his lip during a performance and was unable to continue performing on the trumpet afterward. So he turned his attention to his second instrument, the lute. Being unsatisfied with the pitch pipes commonly used to tune instruments at the time, Shore used his tuning fork (prob- ably an adaptation of the two-pronged eating utensil) to tune his lute before performances, often quipping “I do not have about me a pitch-pipe, but I have what will do as well to tune by, a pitch-fork” (Miller, 1935; Bickerton and Barr, 1987).
It took more than a hundred years before Shore’s tuning fork became an accepted scientific instrument, but starting in the mid-1800s and through the early 1900s, tuning forks
and Helmholtz resonators were two of the most impor- tant items of equipment in an acoustics laboratory. In 1834, Johann Scheibler, a silk manufacturer without a scientific background, created a tonometer, a set of precisely tuned resonators (in this case tuning forks, although others used Helmholtz resonators) used to determine the frequency of another sound, essentially a mechanical frequency ana- lyzer. Scheibler’s tonometer consisted of 56 tuning forks, spanning the octave from A3 220 Hz to A4 440 Hz in steps of 4 Hz (Helmholtz, 1885, p. 441); he achieved this accu- racy by modifying each fork until it produced exactly 4 beats per second with the preceding fork in the set. At the 1876 Philadelphia Centennial Exposition, Rudolph Koenig, the premier manufacturer of acoustics apparatus during the second half of the nineteenth century, displayed his Grand Tonometer with 692 precision tuning forks ranging from 16 to 4,096 Hz, equivalent to the frequency range of the piano (Pantalony, 2009). Keonig’s Grand Tonometer was purchased in the 1880s by the United States Mili- tary Academy and currently resides in the collection of the Smithsonian National Museum of American History (Washington, DC; see For his own personal use, Koenig made a set of 154 forks ranging from 16 to 21,845.3 Hz; he achieved this decimal point preci- sion at a frequency he couldn’t hear by using the method of beats as well as the new optical method developed by Lissajous in 1857 (Greenslade, 1992). Lissajous’ method of measuring frequencies involved the reflection of a narrow beam of light from mirrors attached to the tines of two massive tuning forks, oriented perpendicular to each other, resulting in the images that now bear his name (Guillemin, 1877, p. 196, Fig. 135 is one of the earliest images of Lis- sajous and his optical imaging tuning fork apparatus for creating these figures).
From the beginning, it was observed that touching the stem of the fork to a surface would transmit the vibration of the fork to the surface, causing it to vibrate. In the mid- 1800s, Ernst Heinrich Weber and Heinrich Adolf Rinne
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 48 Acoustics Today • Summer 2020 | Volume 16, issue 2

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