Phase speed ω/k as a function of normalised wavenumber ka for the trapped sausage (top) and kink (bottom) modes in a loop with density contrast ρ₀/ρ_e = 50 (and plasma β = 0). The solid lines are for the slab geometry and the dashed lines are for the cylindrical geometry. The lower and upper dotted lines correspond to the internal Alfvén speed C_A0 and external Alfvén speed C_Ae, respectively. In the lower panel the middle dotted line corresponds to the kink speed C_k.