Due to radiation losses, resonances in open systems are generally complex valued. However,
near symmetric, centred objects in ducted domains, or in periodic arrays, so-called
trapped modes can exist below the cut-off frequency of the first non-trivial duct mode.
These trapped modes have no radiation loss and correspond to real-valued resonances.
Above the first cut-off frequency isolated trapped modes exist only for specific parameter
combinations. These isolated trapped modes are termed embedded, because their
corresponding eigenvalues are embedded in the continuous spectrum of an appropriate
differential operator. Trapped modes are of considerable importance in applications because
at these parameters the system can be excited easily by external forcing. In the
present paper directly computed embedded trapped modes are compared with numerically
obtained resonances for several model configurations. Acoustic resonances are also
computed in two-dimensional models of a butterfly and ball-type valve as examples of
more complicated geometries.