With the Taylor expansion method, we show that it is possible to improve the
lattice Boltzmann method for acoustic applications. We derive a formal
expansion of the eigenvalues of the discrete approximation and fit the
parameters of the scheme to enforce fourth order precision. The corresponding
discrete equations are solved with the help of formal calculus. The solutions
are explicited in the case of D3Q27 lattice Boltzmann scheme. Various numerical
tests support the coherence of this approach.