  For computational acoustics, schemes need to have low-dispersion and
low-dissipation properties in order to capture the amplitude and phase of the
wave correctly. To improve the spectral properties of the scheme, the authors
have previously proposed a scale sensor to automatically adjust the numerical
dissipation. In consequence, a fourth-order finite difference scheme with
minimized dispersion and adaptive dissipation (MDAD) has been proposed [1]. In
this study, we further investigate this method for the high-fidelity numerical
simulation of the acoustic problems and a new dispersion control method is
proposed which is different from the traditional dispersion relation preserving
(DRP) approach. Firstly, the scale sensor, which quantifies the local length
scale of the solution as the effective scaled wavenumber, is modified for
better performance on composite waves. Then the scale sensor is applied to
control both the dispersion and dissipation of the scheme. The relationships
between the dispersion/dissipation parameter and the effective scaled
wavenumber are analytically and artificially constructed respectively. Thus, a
fourth-order finite difference scheme with accurate dispersion and adaptive
dissipation (ADAD) is constructed. The approximate dispersion relation (ADR)
shows that the ADAD scheme achieves accurate dispersion property at k < 2.5.
The dissipation is negligible at low wave number and gradually increases after
k = 1 to suppress non-physical oscillations. Several benchmark cases of
computational acoustics are presented to verify the high resolution of the
proposed scheme compared with the conventional spectral optimized schemes.
