Carbon microphone
The first microphone that enabled proper voice telephony was the (loose-contact) carbon microphone (then called transmitter). This was independently developed around 1878 by David Edward Hughes in England and Emile Berliner and Thomas Edison in the US. Although Edison was awarded the first patent in mid-1877, Hughes had demonstrated his working device in front of many witnesses some years earlier, and most historians credit him with its invention.
Wireless microphone
Another German equipment manufacturer, Beyerdynamic, claims that the first wireless microphone was invented by Hung C. Lin. Called the "transistophone," it went into production in 1962. The first time that a wireless microphone was used to record sound during filming of a motion picture was allegedly on Rex Harrison in the 1964 film "My Fair Lady", through the efforts of Academy Award-winning Hollywood sound engineer George Groves.