Fundamental‐frequency component of a finite‐amplitude plane wave

A method due to Westervelt [Proceedings of the Third International Congress on Acoustics, Stuttgart 1959 (Elsevier, Amsterdam, 1961), Vol. 1, pp. 316–321] is used to describe the fundamental frequency component of an initially sinusoidal finite‐amplitude plane wave. The result, expressed in terms of the extra loss (in decibels) introduced by nonlinearity, is given as 10 log10[1 + Γ2(1 − e−2σ/Γ)2/16] where Γ is the acoustic Reynold's number and σ is range normalized to the shock formation distance. This relation is shown to lie within 1 dB of Blackstock's results obtained from Burgers' equation [D. T. Blackstock, J. Acoust. Soc. Am. 36, 534–542 (1964)].