There are only two physical sound output options for the PS4: Optical (Toslink) and HDMI. You would need to find speakers that have an optical input. However, there are plenty of small soundbars if you have room for one that can accept the optical in for sound.
Another option is to find speakers with the traditional RCA inputs (yellow, red) and then buy an optical to RCA adapter. This of course would put you over $50 between a decent pair of speakers and that adapter. Most PC speakers at or below $50 are pre-wired to connect to a PC's audio out (3.5mm jack) which will not work otherwise.
Your other option is to find some Bluetooth enabled speakers and pair them up to the PS4 like a Bluetooth headset. Here are some from Creative Labs for $55(US).
http/us.creative.com/p/speakers/creative-t12-wireless