Abstract
The propagation of weakly non-linear acoustic waves is studied, which are radiated from a harmonically pulsating sphere in an inviscid perfect gas. A representation of the solution is presented for a far field equation of the first order, which is closely related to the solution obtained by the method of renormalization. The applicability of the method to the present problem is proved within the first order approximation. The asymptotic solution in the far field is obtained up to the second order by using the method of renormalization. A uniformly valid solution is, to the second approximation, constructed by matching the near field solution with the far field solution. Also investigated is the effect of dimensionless parameters and the second order correction on the acoustic shock formation distances and the non-linear distortion of waveforms.
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