Acoustic waves emitted by radial oscillations of a spherical bubble in viscous compressible heat conductive liquids

Conclusion

The relations have been derived which characterize the speed distribution υ(r, t) of density ϱ′(r, t) and pressure p′ir, t) of a viscous thermally conductive liquid, through which a spherical successive acoustic wave has been propagating. At small damping, the wave vector (32) has been determined in the same way as in the case of a planar successive wave [2], i.e.

$$k = \pm \frac{\omega }{{c_0 }}\left( {1 - i\frac{{\omega b}}{{2\varrho _0 c_0^2 }}} \right).$$

((40))

Its imaginary part determines the sound damping as it results from the equation of monochromatic wave (35), whose amplitude of speed at a relatively large distance taken from the bubble decreases according to the following relation

$$v_0 = const\frac{1}{r}\exp \left[ { - \frac{{\omega ^2 b}}{{2\varrho _0 c_0^3 }}(r - R_0 )} \right].$$

((41))

From the relations derived it also follows that in the case of spherical acoustic waves, e.g. in water, parameters η, ζ, and λ do not appear to be too obvious, while e.g. in the case of mercury or liquid metals their influence will be considerable.