  Neural networks have emerged as a tool for solving differential equations in
many branches of engineering and science. But their progress in frequency
domain acoustics is limited by the vanishing gradient problem that occurs at
higher frequencies. This paper discusses a formulation that can address this
issue. The problem of solving the governing differential equation along with
the boundary conditions is posed as an unconstrained optimization problem. The
acoustic field is approximated to the output of a neural network which is
constructed in such a way that it always satisfies the boundary conditions. The
applicability of the formulation is demonstrated on popular problems in plane
wave acoustic theory. The predicted solution from the neural network
formulation is compared with those obtained from the analytical solution. A
good agreement is observed between the two solutions. The method of transfer
learning to calculate the particle velocity from the existing acoustic pressure
field is demonstrated with and without mean flow effects. The sensitivity of
the training process to the choice of the activation function and the number of
collocation points is studied.
