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The one-dimensional bubble: an unusual oscillator, with applications to human bioeffects of underwater sound

The one-dimensional bubble: an unusual oscillator, with applications to human bioeffects of underwater sound
The one-dimensional bubble: an unusual oscillator, with applications to human bioeffects of underwater sound
In this paper the oscillation dynamics of a linear gas pocket in a liquid are analysed. These include several features of potential use at undergraduate level for illustrating characteristics beyond those normally encountered in expositions of simple harmonic oscillators. The oscillator in question is unusual first in that, as with all gas bubbles in liquid, the inertia is invested primarily in the surrounding liquid, rather than in the pocket itself. Second, a nonlinearity arises through the displacement dependence of the oscillator stiffness. These effects are included in the equation of motion of a damped, forced, one-dimensional bubble, which is solved numerically. Analytical solutions for the natural frequency of small-amplitude undamped oscillations in the linear limit are also obtained, and both are compared with experimental measurements of the phase and amplitude response of a laboratory one-dimensional bubble. The analysis is used to indicate the response of air bubbles within the ear canals of divers to low frequency underwater sound, and the potential of bubbles in lung blood vessels to cause haemorrhage when subjected to lithotripsy.
0143-0807
275-281
Leighton, T.G.
3e5262ce-1d7d-42eb-b013-fcc5c286bbae
White, P.R.
2dd2477b-5aa9-42e2-9d19-0806d994eaba
Marsden, M.A.
837da135-c914-41cd-bf3f-567432858c1b
Leighton, T.G.
3e5262ce-1d7d-42eb-b013-fcc5c286bbae
White, P.R.
2dd2477b-5aa9-42e2-9d19-0806d994eaba
Marsden, M.A.
837da135-c914-41cd-bf3f-567432858c1b

(1995) The one-dimensional bubble: an unusual oscillator, with applications to human bioeffects of underwater sound. European Journal of Physics, 16 (6), 275-281. (doi:10.1088/0143-0807/16/6/006).

Record type: Article

Abstract

In this paper the oscillation dynamics of a linear gas pocket in a liquid are analysed. These include several features of potential use at undergraduate level for illustrating characteristics beyond those normally encountered in expositions of simple harmonic oscillators. The oscillator in question is unusual first in that, as with all gas bubbles in liquid, the inertia is invested primarily in the surrounding liquid, rather than in the pocket itself. Second, a nonlinearity arises through the displacement dependence of the oscillator stiffness. These effects are included in the equation of motion of a damped, forced, one-dimensional bubble, which is solved numerically. Analytical solutions for the natural frequency of small-amplitude undamped oscillations in the linear limit are also obtained, and both are compared with experimental measurements of the phase and amplitude response of a laboratory one-dimensional bubble. The analysis is used to indicate the response of air bubbles within the ear canals of divers to low frequency underwater sound, and the potential of bubbles in lung blood vessels to cause haemorrhage when subjected to lithotripsy.

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Published date: 1995
Organisations: Acoustics Group

Identifiers

Local EPrints ID: 349531
URI: http://eprints.soton.ac.uk/id/eprint/349531
ISSN: 0143-0807
PURE UUID: feba14cd-9f97-4769-8de1-15c116bff975
ORCID for T.G. Leighton: ORCID iD orcid.org/0000-0002-1649-8750
ORCID for P.R. White: ORCID iD orcid.org/0000-0002-4787-8713

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Date deposited: 07 Mar 2013 09:53
Last modified: 06 Jun 2018 13:12

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