The council of any city shall have power to compel the attendance of witnesses before the mayor and council or any committee thereof in any investigation ordered by the council: provided, that all process shall be issued by the mayor, and the attendance of such witnesses may be compelled by attachment, fine, or imprisonment; provided, further, that the mayor or president of the council shall preside at such hearing and administer all oaths and any person testifying falsely at such investigation shall be deemed guilty of perjury.