  The normal mode model is important in computational atmospheric acoustics. It
is often used to compute the atmospheric acoustic field under a harmonic point
source. Its solution consists of a set of discrete modes radiating into the
upper atmosphere, usually related to the continuous spectrum. In this article,
we present two spectral methods, the Chebyshev--Tau and Chebyshev--Collocation
methods, to solve for the atmospheric acoustic normal modes, and corresponding
programs were developed. The two spectral methods successfully transform the
problem of searching for the modal wavenumbers in the complex plane into a
simple dense matrix eigenvalue problem by projecting the governing equation
onto a set of orthogonal bases, which can be easily solved through linear
algebra methods. After obtaining the eigenvalues and eigenvectors, the
horizontal wavenumbers and their corresponding modes can be obtained with
simple processing. Numerical experiments were examined for both downwind and
upwind conditions to verify the effectiveness of the methods. The running time
data indicated that both spectral methods proposed in this article are faster
than the Legendre--Galerkin spectral method proposed previously.
