Here in Europe tv sets from early 70 to mid 80 used ultrasonic remote controls. All of these were entirely transistorized units and usually worked with a 9v battery. Functions were usually channel change (they didn't actually change channels but let the user choose directly between usually 7,8,12 or 16 memories where one could store favorite channels),volume,brightness,color intensity,sound mute, reset,on/off. Other less usual functions could be the recall of clock on screen or tone adjustment.
Remote tuning on ultrasonic remotes came on late models just before this technology went out to leave space for infra red remotes. Here are few tipe of european ultrasonic remote controls. (pict.1 left: Telefunken supersonic 200. right: Loewe Sensotronic. pict.2 left

umont. center:Nordmende.right:B&O Beovision control module.)