History

By nonlinearity an originally monochromatic acoustic wave develops into a sawtooth wave with shocks, containing all integer number multiples of the original frequency.

Manifestations of nonlinear acoustics are known since the 18th century. An early example is the musical phenomenon called Tartini tones, discovered in 1714 by the violinist Tartini (1692-1770).

When two tones are sounded loudly and simultaneously on the violin, the tone with the difference frequency is heard.

The nonlinear origin of combination tones, of which the difference frequency tone is an example, was realized by Helmholtz (1821-1894). Large amplitude mechanical vibrations were studied already by Euler (1707-1778).

The correct description of large amplitude waves had to wait for the insight that the acoustic disturbances are adiabatic and not isothermal. This description of nonviscous nonlinear acoustic waves made great progress in the middle of the 19th century by works by Airy, Earnshaw and Riemann.

Another nonlinear acoustic phenomenon early studied is shock formation. The main contributions to the description of the wave after the formation of the shock were made by Rankine (1870) and Hugoniot (1887). The need to include viscosity in the description of the shock was realized already by Stokes (1848), but the first successful attempts were made by Lord Rayleigh (1910) and Taylor (1910).

The mathematical analysis of the sawtooth wave, which develops from an original monochromatic plane propagating wave, was made in the 1930's. For propagation in a nonviscous fluid the solution was given by Fubini-Ghiron (1935) and for propagation in a viscous fluid the solution was given already in 1931 by Fay.

Fay's solution was found without using Burgers' equation, which is the most important nonlinear acoustics wave equation and which is satisfied by Fay's solution. Burgers' equation, together with its generalizations and modifications, is the dominating wave equation for propagating waves in nonlinear acoustics.

The development of nonlinear acoustics as a specialty in its own right began in the 1950's. It started with methods for generation and measurement of sound waves with large amplitude and with new methods for their description, founded on Burgers' equation and its generalizations. The first International Symposium on Nonlinear Acoustics (ISNA) was held in 1968. Some of the most important examples of the development of nonlinear acoustics during the latest 50 years are:

1) Mathematical and numerical methods have improved and can be used for describing more and more large amplitude wave phenomena, both standing and propagating waves, in gases, liquids and solids with different constitutive properties.

2) Nonlinear wave phenomena are studied together with flow, turbulence and thermodynamics.

3) Nonlinear wave phenomena in different kinds of media are important in atmosphere physics, oceanography, seismology as well as in medicine, where high-intensity sound beams are used in diagnostics and therapy. Other examples are use of nonlinear waves in communication and music.

4) Nonlinear elastic properties of materials are important for deformation. Frequently testing uses nonlinear acoustic waves.

5) Acousto-optical phenomena are studied in crystals and liquids.

6) Nonlinear waves are studied in multiphase media, especially cavitating and bubbly media.

7) Devices are developed and used for industrial applications of nonlinear acoustics.

It is expected that in the 18th ISNA 7-10 July, 2008, in Stockholm, Sweden, interesting new achievements will be presented in the research areas mentioned above as well as in new fundamental and applied research areas of nonlinear acoustics.

The venues of the International Symposia on Nonlinear Acoustics (ISNA) are:

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