Dispersion diagrams for the analysed loops showing the phase speed V_p of the kink and sausage modes as a function of the normalised wavenumber kR. The upper, middle, and lower dotted lines represent C_Ae, C_k, and C_A0, respectively. A logarithmic scale is used to emphasise the behaviour in the long wavelength limit kR ≪ 1. The dashed lines correspond to the value for the global standing mode kR = πR/L.