We study high energy resonances for the operator when V has strong frequency dependence. The operator is a Hamiltonian used to model both quantum corrals (Aligia and Lobos 2005 J. Phys.: Condens. Matter 17 S1095, Barr 2010 Nano Lett. 10 3253–60) and leaky quantum graphs (Exner P 2008 Analysis on Graphs and its Applications (Providence, RI: American Mathematical Society) pp 523–564). Since highly frequency dependent delta potentials are out of reach of the more general techniques in (Galkowski J 2015 arXiv:1511.05894, Galkowski J and Smith H 2014 Int. Math. Res. Not.) we study the special case where and with . Here is the frequency. We give sharp bounds on the size of resonance free regions for and the location of bands of resonances when . Finally, we give a lower bound on the number of resonances in logarithmic size strips: .