JUST BECAUSE I'VE BEEN ASKED: Yes, there is a electrical cord that has to be plugged in. The wireless connection is between the powered amp (speaker) and the receiver / transmitter (mic).
IR is limited by line of sight and sometimes experiences interference with over-saturation of direct sunlight, & other wireless signals /radio frequencies.
While not often professionally deployed, it's a cheap wireless technology that still does have applications and people who like to use it.