Notes to Lindsay's Acoustics - Historical and Philosophical Development - Introduction

I. Production of Sound

Vibrating String

Brook Taylor (1685-1731)

author of Taylor’s theorem on infinite series

From the equation of this curve and the Newtonian equation of motion, he was able to derive a formula for the frequency of the fundamental vibration that agreed with the experimental law of Mersenne and Galileo.

Jean Le Rond d’Alembert (1717-1783), and Leonhard Euler (1707-1783)

set up the partial differential equation of motion of the vibrating string and to solve it in what is essentially the modern fashion.

Newton and Leibniz were unable to handle the motions of continues media

The Vibrating String As A Source Of Sound

John Wallis (1616-1703) and Joseph Sauveur (1653-1716)

  • Dr. Wallis’s letter to the publisher, concerning a new musical discovery; written from Oxford, March 14. 1676/7: https://soundandscience.net/texts/dr-walliss-letter-to-the-publisher-concerning-a-new-musical-discovery-written-from-oxford-march-14-1676-7/

a stretched string can vibrate in parts so that at certain intermediate points, which Sauveur called nodes, no motion ever takes place, whereas very violent motion takes place at intermediate points called loops.

such vibrations correspond to higher frequencies than that associated with the simple vibration of the string as a whole without nodes, and indeed that these frequencies are integral multiples of the frequency of the simple vibration.

Those emitted sounds (nodes) were called harmonic tones called by Sauveur. The sound corresponding to the simple vibration was called fundamental.

Daniel Bernoulli

who explained that

a vibrating string could produce the sounds corresponding to several of its harmonics at the same time.

it is possible for a string to vibrate in such a way that a multitude of simple-harmonic oscillations are present at the same time and that each contributes independently to the resultant vibration, the displacement at any point of the string at any instant being the algebraic sum of the displacements associated with the various simple-harmonic modes.

the principle of superposition

Bernoulli: Bernoulli introduced the famous principle of the coexistence of small oscillations, also referred to as the principle of superposition.

Euler: The real significance of the superposition principle was pointed out almost immediately by Euler*: namely, that the partial differential equation that governs the motion of the ideal frictionless string is linear. With this understanding, the superposition principle can be proved as a theorem.

Fourier: The possibility of expressing any arbitrary function—e.g., the initial shape of a vibrating string in terms of an infinite series of sines and cosines, implied by the superposition theorem—was hard to accept in terms of mid-18th century mathematics. It was only in 1822 that J. B. J. Fourier [267] (1768-1830), in his analytical theory of heat, based his celebrated theorem on this type of expansion with consequences of the greatest value for the advancement of acoustics.

J. L. Lagrange

Mécanique analytique, Analytical Mechanics.

d’Alembert

Wave equation

Sounds Produced By Organ Pipes And Musical Wind Instruments

  • Euler: 1727, Physical Dissertation on Sound (earlier than Lagrange)
  • 1759: there was considerable activity by both Euler and Lagrange on the subject of sound oscillations in tubes and much correspondence between them.
  • 1766: Euler produced an elaborate treatise on fluid mechanics, the fourth section [24] of which was entirely devoted to sound waves in tubes.

The Vibrations Of Metal Bars, Plates, And Shells

Robert Hooke

  • Robert Hooke, 1660 discovered, in 1675 announced in the form of the anagram CEIIINOSSSTTUV, ut tensio sic vis, connecting the stress and strain for bodies undergoing elastic deformations.
    • This law forms the basis for the whole mathematical theory of elasticity, including elastic vibrations giving rise to sound.
    • The mathematical methods used were later systematized and extended by Lord Rayleigh in his Theory of Sound.

E. F. F Chladni (1756-1824)

  • 1787, Entdeckungen über die Theorie des Klanges,
  • 1802, Die Akustik

Marie-Sophie Germain (1776-1831)

  • the correct fourth-order equation

Gustav R. Kirchhoff (1824-1887)

https://wikiless.deep-swarm.xyz/wiki/Gustav_Kirchhoff?lang=en

The Vibrations Of A Flexible Membrane

S. D. Poisson (1781-1840)

  • first solution of the analogous problem of the vibrations of a flexible membrane, important for the understanding of the sounds emitted by drums
  • failed to complete the case of the circular membrane

R. F. A. Clebsch (1833-1872)

  • 1862, complete the case of the circular membrane

Electroacoustics

The ability to excite vibrations in media of arbitrary nature, size, and shape and with arbitrary frequency over a wide range had to await the development of electroacoustics, largely a product of 20th-century research.

General History

  • electrical oscillations and oscillating electric circuits were discovered and invented in the middle of the 19th century,
  • methods of coupling them to mechanical systems so as to make them produce mechanical oscillations did not arise in a practical fashion until after 1900.
  • tuning forks as frequency standard sound sources

the Curie brothers (1855-1941,1859-1906) - Magnetic field in 1820's

  • 1880, the Curie brothers, piezoelectric effect experiments: some crystals (notably quartz), of having electric charges appear on the faces when subjected to mechanical stresses of various kinds, and conversely of changing dimensions (i.e., exhibiting strain) when placed in an electric field.

James Prescott Joule (1818-1892)

https://wikiless.deep-swarm.xyz/wiki/James_Prescott_Joule?lang=en#Published_work

  • the magnetostriction effect, i.e., the tendency of magnetizable materials to change dimensions when placed in a magnetic field.
  • 1842, advent of the vacuum-tube oscillator and amplifier

J.W.S Rayleigh (1842-1919)

  • 1877, The Theory of Sound

Human Speech & Animal Sounds

the vocal chords leading to speech in human beings and the noises emitted by lower animals. It is a curious fact that, though these examples of sound production are in may ways the most obvious of all, little attention was paid to them during the historical evolution of acoustics just surveyed.

Basic Mechanism Of Human Speech

  • laryngoscope: 1629, W. Babington, observed the motions of the vocal chords by means of light reflected from mirrors in the mouth. https://journals.sagepub.com/doi/pdf/10.1177/0310057X150430S103
  • perfected laryngoscope: 1857, J. N. Czermac.
  • D. W. Famnsworth, Bell Telephone Lab, movies of the vocal chords. (cannot find source)

Vowel Sounds Of Speech And Singing

Hermann von Helmholtz (1821-1894)

  • 1862, Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik
  • mentioned human hearing

Sir Charles Wheatstone (1802-1875)

a harmonic theory for the production of vowel sounds.

the vocal chords vibrate so as to produce both a fundamental frequency and numerous harmonics. It was assumed that these vibrations when communicated to the air are reinforced by resonance in the mouth cavities.

W. T. Willis

  • 1829, the origin of the vowel sound was not in the continuous vibration of the vocal chords, but rather in puffs of air emitted by them.

Alexander Graham Bell (1847-1922)

the whole oral cavity acts as a single resonator

(... the last section need to be further reviewed)

II. Propagation of Sound

Ancient: sound is conveyed from one point in space to another through some activity of the air.

  • Aristotle, De Anima and De Audibilibus: there is actual motion of air involved, and sound is due to compressional waves in air
  • Marcus Vitruvius Pollio, 1BC, had an adequate grasp of the wave theory of sound in the analogies that he drew with surface waves on water.
  • later philosophers denies views of Aristotle and Vitruvius, who both think in the transmission of sound the air has motion

Near Modern

Pierre Gassendi (1592-1655)

atomic theory, attributed the propagation of sound to the emission of a stream of very small, invisible particles from the sounding body, which, after moving through the air, are able somehow to affect the ear. https://doi.org/10.1119/1.1990711

17th, Source And The Medium In Acoustic Propagation

Otto von Guericke (1602-1686) and Athanasius Kircher (1602-1680)

  • Otto von Guericke (1602-1686), doubt that sound is conveyed by a motion of the air, observing that it is transmitted better when the air is still than when there is a wind.
    • the bell in vacuo experiment: ringing a bell in a jar that was evacuated by means of his air pump, and claimed that he could still hear the sound.
  • Athanasius Kircher (1602-1680), air is not necessary for the transmission of sound
    • the first to try the bell in vacuo experiment
    • 1650, Musurgia Universalis, air is not necessary for the transmission of sound

the trouble with the investigations of von Guericke and Kircher was the failure to avoid transmission through the walls of the vessel coupled with the rather inadequate vacuum they were able to obtain.

Robert Boyle (1627-1691)

  • 1660, repeated the experiment with a much improved air pump and more-careful arrangements, finally observed the now well-known decrease in the intensity ​of the sound as the air is pumped out.
  • concluded that the air is a medium for the transmission of sound, though presumably not the only one.
  • this explanation of the experiment, though hallowed by tradition, is a mistaken one.
  • Actually, impedance mismatch between source and surrounding fluid medium: The observed decrease in the intensity of the sound is due not so much to the failure of the low pressure air to transmit sound as to the increasing difficulty of getting the sound out of the bell (or other sound source) into the air and then out again from the air to the glass container.

Velocity of Sound Propagation

Pierre Gassendi (1592-1655) & Marin Mersenne (1588-1648)

1635, Gassendi made measurements of the velocity of sound in air using firearms and assuming that the light of the flash is transmitted instantaneously.

Later Mersenne showed that Gassendi’s figure was too high

Gassendi:

  • found the velocity is independent of the pitch of the sound, thus discrediting the view of Aristotle, who had taught that high notes are transmitted faster than low notes.
  • made the mistake of believing that the wind has no effect on the measured velocity of sound.

G. A. Borelli (1608-1679) and his colleague V. Viviani (1622-1703)

1650, same experiment.

Conclusion

All these measurements suffered from lack of reference to the temperature, humidity, and wind velocity.

W. Derham (1657-1735)

1708, extensive measurements of the velocity of sound, concluded that the velocity is independent of all environmental conditions except wind.

G. L. Bianconi (1717-1781)

Showed Derham was wrong.

in 1740 demonstrated definitely that the velocity of sound in air increases with the temperature.

First Open-Air Measurement (1738)

1738, The first open-air measurement (no wind) that can be considered at all precise in the modern sense was probably that carried out under the direction of the Academy of Sciences of Paris, using a cqannon as the source of sound.

More sources on Sound Propagation:

Additional Sources Used

  • Andrew Barker, Greek Musical Writings Volume II: Harmonic and Acoustic Theory