A note on the derivation of the wave equation in an inhomogeneous ocean

Several derivations of the wave equation in an inhomogeneous medium appear in the literature. A term ∇p1⋅∇lnρ0 is found in all of them. Inhomogeneities in the sea are due to both gravity and other effects. The reference state characterized by ρ0(xyz) gives rise to two different limits, one due to gravity alone and the other due to inhomogeneities ignoring gravity. Both lead to the same form of the wave equation, but different arguments are required to demonstrate that ∇p1⋅∇lnρ0 can be ignored. A seldom cited paper by Bergmann [J. Acoust. Soc. Am. 17, 329–333 (1946)] is used.