A member of the Welsh Language Society, Cymdeithas yr Iaith Gymraeg, has been given five days' custody for refusing to pay compensation to a radio station.
Gwenno Teifi is the grand-daughter of the late Gwynfor Evans
Gwenno Teifi, 19, was previously told to pay £200 compensation to Radio Carmarthenshire after damaging equipment in a protest.
Ms Teifi, a grand-daughter of ex-Plaid Cymru president Gwynfor Evans, was sentenced by Carmarthen magistrates.
Cymdeithas said she was its first member to receive custody in 10 years.
Ms Teifi, from Llanfihangel-ar-Arth, Carmarthenshire, was initially ordered to pay compensation after taking part in the protest in July 2004.
The demonstration was over the level of Welsh-language output on Radio Carmarthenshire.
The University of Wales Aberystwyth student will serve her sentence at a young offenders' unit in Gloucester.
On Tuesday, the day after she was sentenced, 28 students at Aberystwyth and Bangor universities said they would be going on hunger strike in her support until her release.