Tunable broadband multi-function acoustic metasurface by nested resonant rings

•A kind of tunable subunit named nested resonant rings (NRRs) is proposed.•The NRRs has a broadband bandwidth which can realize 2π phase range covering from 1000 Hz −8000 Hz.•Tunable acoustic metasurface is realized by 19 NRRs and can work in a broadband.•The proposed tunable acoustic metasurface has been demonstrated in abnormal reflection, illusion and focusing.