Savarts Toothed Wheel - BITM - Calcutta 2000 009

The Savart wheel is an acoustical device named after the French physicist

Félix Savart Félix Savart (; ; 30 June 1791, Mézières – 16 March 1841, Paris) was a French physicist and mathematician who is primarily known for the Biot–Savart law of electromagnetism, which he discovered together with his colleague Jean-Baptist ...

(1791–1841), which was originally conceived and developed by the English scientist

Robert Hooke Robert Hooke (; 18 July 16353 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist, and architect. He is credited as one of the first scientists to investigate living ...

(1635–1703). A card held to the edge of a spinning toothed wheel will produce a tone whose pitch varies with the speed of the wheel. A mechanism of this sort, made using brass wheels, allowed Hooke to produce

sound wave In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...

s of a known

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

, and to demonstrate to the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

in 1681 how pitch relates to frequency. For practical purposes Hooke's device was soon supplanted by the invention of the

tuning fork A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs ( ''tines'') formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it ag ...

. About a century and a half after Hooke's work, the mechanism was taken up again by Savart for his investigations into the range of human hearing. In the 1830s Savart was able to construct large, finely-toothed brass wheels producing frequencies of up to 24

kHz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base uni ...

that seem to have been the world's first artificial ultrasonic generators. In the later 19th century, Savart's wheels were also used in physiological and psychological investigations of time perception. Nowadays, Savart wheels are commonly demonstrated in physics lectures, sometimes driven and sounded by an air hose (in place of the card mechanism).

Description

The basic device consists of a ratchet-wheel with a large number of uniformly spaced teeth. When the wheel is turned slowly while the edge of a card is held against the teeth a succession of distinct clicks can be heard. When the wheel is spun rapidly it produces a shrill tone, whereas if the wheel is allowed to turn more slowly the tone progressively decreases in pitch. Since the frequency of the tone is directly proportional to the rate at which the teeth strike the card, a Savart wheel can be calibrated to provide an absolute measure of pitch. Multiple wheels of different sizes, carrying different numbers of teeth, can also be attached so as to allow several pitches (or

chords Chord or chords may refer to: Art and music * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord, a chord played on a guitar, which has a particular tuning * The Chords (British band), 1970s British mod ...

) to be produced while the axle is being turned at a constant rate.

Hooke's wheel

Hooke began work on his wheel in March 1676, in conjunction with the renowned clockmaker Thomas Tompion, following conversations with the music theorist

William Holder William Holder Royal Society, FRS (1616 – 24 January 1698) was an English clergyman and music theorist of the 17th century. His most notable work was his widely known 1694 publication ''A Treatise on the Natural Grounds and Principles of Harmon ...

. He had a longstanding interest in musical vibrations, and a decade earlier in 1666 had even boasted to

Samuel Pepys Samuel Pepys ( ; 23 February 1633 – 26 May 1703) was an English writer and Tories (British political party), Tory politician. He served as an official in the Navy Board and Member of Parliament (England), Member of Parliament, but is most r ...

that he could tell the rate a fly's wings were beating from the sound they made. In July 1681, he demonstrated to the

his new device for producing distinct

musical tone Traditionally in Western classical music, Western music, a musical tone is a steady periodic function, periodic sound. A musical tone is characterized by its duration (music), duration, pitch (music), pitch, amplitude, intensity (or loudness), an ...

s by striking the teeth of fast-turning brass wheels. In this way, he was able to generate for the first time

s of known

, and provide an empirical demonstration of the correspondence between the

human perception Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous syste ...

of pitch and the

physical property A physical property is any property of a physical system that is measurable. The changes in the physical properties of a system can be used to describe its changes between momentary states. A quantifiable physical property is called ''physical ...

of sound-wave frequency. Furthermore, by fitting different wheels alongside one another on the same axis, he was able to verify frequency ratios for musical intervals, such as

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval f ...

s and fourths, etc. Hooke published his findings in 1705. Despite providing an objective measure of pitch, for everyday use his wheel was soon made irrelevant by the invention in 1711 of the

Savart's version

Hooke's device was not used again for study purposes for over a century. Its next documented usage was in 1830 when Savart reported his use of a system similar to Hooke's which he developed while investigating the lower range of

human hearing Hearing, or auditory perception, is the ability to perceive sounds through an organ, such as an ear, by detecting vibrations as periodic changes in the pressure of a surrounding medium. The academic field concerned with hearing is auditory sc ...

. Savart's specific contribution was to attach a

tachometer A tachometer (revolution-counter, tach, rev-counter, RPM gauge) is an instrument measuring the rotation speed of a axle, shaft or disk, as in a motor or other machine. The device usually displays the revolutions per minute (RPM) on a calibrat ...

to the axis of the toothed wheel to facilitate calibration of the tooth rate. Savart used his wheel as a practical alternative to John Robison's siren, which was also being adopted at the time by

Charles Cagniard de la Tour Baron Charles Cagniard de la Tour (31 March 1777 – 5 July 1859) was a French engineer and physicist. Charles Cagniard was born in Paris, and after attending the École Polytechnique became one of the ''ingénieurs géographiques''. He examined t ...

to test the range of human hearing. By 1834 Savart was constructing brass wheels with a width of 82 cm, containing as many as 720 teeth. These wheels, which could produce frequencies up to 24

, have been tentatively proposed as the first artificial generators of

ultrasound Ultrasound is sound with frequency, frequencies greater than 20 Hertz, kilohertz. This frequency is the approximate upper audible hearing range, limit of human hearing in healthy young adults. The physical principles of acoustic waves apply ...

Use in time perception experiments

In the later 19th century, Savart's wheel was adapted for use in physiological and psychological investigations of the human

perception of time In psychology and neuroscience, time perception or chronoception is the subjective experience, or sense, of time, which is measured by someone's own perception of the duration of the indefinite and unfolding of events. The perceived time interval b ...

. In 1873, the Austrian physiologist Sigmund Exner reported the auditory ability to distinguish successive clicks from the wheel (or, alternatively, rapidly snapped electric sparks) at time intervals as close as 2

millisecond A millisecond (from '' milli-'' and second; symbol: ms) is a unit of time in the International System of Units equal to one thousandth (0.001 or 10−3 or 1/1000) of a second or 1000 microseconds. A millisecond is to one second, as one second i ...

s (1/500 sec). A modified wheel that produced varying numbers of clicks at different intervals was later used by the American psychologists

G. Stanley Hall Granville Stanley Hall (February 1, 1844 – April 24, 1924) was an American psychologist and educator who earned the first doctorate in psychology awarded in the United States of America at Harvard University in the nineteenth century. His ...

and

Joseph Jastrow Joseph Jastrow (January 30, 1863 – January 8, 1944) was a Polish-born American psychologist renowned for his contributions to experimental psychology, design of experiments, and psychophysics. He also worked on the phenomena of optical illu ...

, who in 1886 reported on the limits to the human perception of acoustic discontinuities.

Musical and other applications

In 1894, French electrical engineer

Gustave Trouvé Gustave Pierre Trouvé (2 January 1839 – 27 July 1902) was a French electrical engineer and inventor in the 19th century. A polymath, he was highly respected for his innovative skill in miniaturization. Early life and education Gustave Trouvé ...

patented an electrically (or clockwork) powered keyboard instrument capable of playing a series of 88 variously-sized Savart wheels from a piano keyboard, allowing harmonic chords and dynamics. The same principle is used in modern-day electromechanical organs, such as the

Hammond organ The Hammond organ is an electric organ invented by Laurens Hammond and John M. Hanert, first manufactured in 1935. Multiple models have been produced, most of which use sliding #Drawbars, drawbars to vary sounds. Until 1975, sound was created ...

, that make use of

tonewheel A tonewheel or tone wheel is a simple electromechanical apparatus used for generating electric musical notes in electromechanical electronic organ, organ instruments such as the Hammond Organ, Hammond organ and in telephony to generate audible ...

s. The concept has also been adapted to produce an

experimental musical instrument An experimental musical instrument (or custom-made instrument) is a musical instrument that modifies or extends an existing instrument or class of instruments, or defines or creates a new class of instrument. Some are created through simple modif ...

created by Bart Hopkin. This application of Savart's wheel consists of a series of 30 wooden disks of increasing size mounted on a motorized axle. Rasping vibrations are induced in a

plectrum A plectrum is a small flat tool used for plucking or strumming of a stringed instrument. For hand-held instruments such as guitars and mandolins, the plectrum is often called a pick and is held as a separate tool in the player's hand. In harpsic ...

when it comes into contact with the ridges that line each disk at regular intervals, and are amplified in a

styrofoam Styrofoam is a brand of closed-cell extruded polystyrene foam (XPS), manufactured to provide continuous building insulation board used in walls, roofs, and foundations as thermal insulation and as a water barrier. This material is light blue in ...

cup which acts as a

sounding board A sounding board, also known as a tester and abat-voix is a structure placed above and sometimes also behind a pulpit A pulpit is a raised stand for preachers in a Christian church. The origin of the word is the Latin ''pulpitum'' (platf ...

. The instrument is claimed to make "the most obtrusive, obnoxious and irritating

sound In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the br ...

ever known." Nowadays, Savart wheels are commonly used for demonstrations during physics lectures. In one variant, the wheel can be driven by an air hose blowing on the teeth; in this case, the pitch of the sound produced will vary with the force of the air current.

Notes and references

Notes References

External links

"Savart's Wheel" – musical instrument designed by Bart Hopkin
{{Plucked idiophones Acoustics Pitch (music) Physics experiments Ultrasound Experimental musical instruments Mechanical musical instruments Lamellophones