Ray‐tracing simulations and estimates of whistler wave damping show that magnetospherically reflected whistlers can persist for ∼102 s in a low frequency band (ƒ ∼1 kHz). The combined contribution from whistler rays produced by a single lightning flash but entering the magnetosphere at different points form a continuous hiss‐like signal, as observed at a fixed point. Estimates indicate that the total whistler wave energy input into the magnetosphere from lightning discharges may maintain experimentally observed levels of magnetospheric hiss.