The Murfee Resonator
Thomas B. Greenslade, Jr.
Kenyon College, Gambier, Ohio 43022
Mills College, Oakland, California 94613
How do you tune a piano? Absent perfect pitch, the piano tuner uses a tuning fork (ref. 1) as a reference to adjust one set of identical strings to the same frequency, and expands the tuning from there. But other devices can be used to produce a known frequency, including the Murfee resonator, patented in 1912 by a scientific man of all work, Edward H. Murfee.
A complete Murfee resonator has been preserved at Mills College, and is shown in Fig. 1. The instrument is a calibrated quarter-wave resonator, and can be used both to detect unknown
frequencies and produce known frequencies of sound. It was an expensive instrument, costing $65 in 1912, which corresponds to about $1000 in present-day currency.
The patent drawing in Fig. 2 shows the basic operation of the instrument: The cylinder is 4 cm in diameter and about 32.5 cm in length. The piston is driven up and down the cylinder by the cog
wheel that engages the rack attached to the piston rod; this mechanism can be seen in the close- up of the instrument in Fig. 3. The open end of the cylinder is held toward the source of the sound, and the piston adjusted until resonance is obtained. The piston rod is hollow, and the sound is detected by pressing the blue cone shown on the right-hand side of Fig. 3 against the user’s ear. Alternately, a rubber tube can be attached to the cone and the sound conveyed to both ears using a stethoscope-type arrangement.
For those with a background in physics: the vibration of an object at the open end of the cylinder sends sound waves toward the piston, which reflects sound waves back. The wave inside the cylinder is thus a standing wave: the sum of two waves moving in opposite directions. Because the piston end of the tube is closed, this end is a pressure antinode, a place where pressure can undergo its greatest fluctuations. Pressing the cone at the end of the central tube to the ear causes sound due to the eardrum’s resulting vibration.
The man in Fig. 4 is using the resonator to determine the frequency of a buzzer. He is directing the open end of the resonator toward the buzzer and using acoustical earphones to locate a resonance. He will then look at the reading of the plunger to get the depth of the resonating cavity, add 0.6 cm (a small correction required by the fact that the pressure node is not quite at the cylinder’s open end), and multiply by four (adjacent nodes and antinodes are one-quarter of a wavelength apart) to get the wavelength. The frequency is then the speed of sound (about 344.2 m/s at room temperature) divided by the wavelength.
The buzzer in Fig. 4 is a piece of standard apparatus that Murfee had in his Brenau College physics laboratory, and is shown in Fig. 5. This is a set of separable helices: a small coil that is placed inside the larger coil, with a make and break contact mechanism mounted on the base to take the direct current from the battery on the table in Fig. 4 and convert it to alternating current. The make and break mechanism hums in use, and it is being used as a source of sound of a definite frequency.
Figure 6, taken from the advertising brochure for the resonator, shows a piano being tuned with the aid of the resonator that is lying just above the keyboard.
Edward Hunter Murfee (1845-1932) was a child of the American South. He was born in Southampton County, Virginia, just a few miles inland from Virginia Beach. In 1862 he entered the University of Alabama, and had to leave when the University closed because of the Civil War; he later returned and finished his degree. In his subsequent career he seemed to jump rapidly between widely divergent positions. He was a schoolmaster in Demopolis, Alabama, and then a distributor for a plow invented by his father. In 1871 he became the Professor of Military Engineering and Commandant of Cadets at the University of Alabama; the next year he was the Professor of English at Union University in Murfreesboro, Tennessee. By 1885 he was the Professor of Mathematics and Logic at the Arkansas Industrial University, which was founded in 1871 and became the University of Arkansas in 1899.
At the Fayette, Arkansas institution he was the senior professor and was appointed the Acting President in 1887; a year later he became the President and Chancellor. Murfee left Arkansas in 1894 and became the President of Alabama Central College in Tuscaloosa, Alabama. Six years later he was elected the President of the Greenville, South Carolina Female College; two years later he founded the Ashville (North Carolina) Seminary and later was the President of Boscobel College in Nashville, another school for young women. He finished his career with twenty five years as the head of the science department at Brenau College in Gainesville, Georgia.
1. “John Shore in 1711 had a place as trumpeter in the Band of Queen Anne … later he was Lutenist in the Chapel Royal. He was the original inventor of the tuning fork; he always carried one with him to tune his lute by, which, whenever he used it, gave rise to a pun. At a concert he would say: “I do not have about me a pitch-pipe, but I have what will do as well to tune by, a pitch-fork,” From Dayton Clarence Miller, Anecdotal History of the Science of Sound (The Macmillan Company, New York, 1935), p39.