what mode of communication did they use?
The radio communication system
Voyager 1
The radio communication system of Voyager 1 was designed to be used up to and beyond the limits of the Solar System. 
when did voyager 1 leave our solar system August 25, 2012 what was its mission or destination? Part of the Voyager program to study the outer Solar System, also the probe's objectives included flybys of Jupiter, Saturn, and Saturn's largest moon, Titan.
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Voyager 1 [SEP] Communication system
The radio communication system of Voyager 1 was designed to be used up to and beyond the limits of the Solar System. The communication system includes a diameter high gain Cassegrain antenna to send and receive radio waves via the three Deep Space Network stations on the Earth. The craft normally transmits data to Earth over Deep Space Network Channel 18, using a frequency of either 2.3 GHz or 8.4 GHz, while signals from Earth to Voyager are transmitted at 2.1 GHz. When Voyager 1 is unable to communicate directly with the Earth, its digital tape recorder (DTR) can record about 67 megabytes of data for transmission at another time.