[rotorwrench]

Two way radio sets were around in 1934 but they were big bulky sets with several housings for the different operations they performed. They weren't designed for cars but many were battery operated with big bulky batteries so it's feasible that one could be carried in a car. They likely would have to stop and set it up before they could transmit. They could string a wire for an antenna. Range would not have been very far anyway. In 1936 Motorola came out with their first police cruiser radio but it was just a receiver set. Their first 2-way came out in 1939.

There were optional Grigsby-Grunow radios for 1932 Ford cars but the tuner head fit on the steering column. By 1934, there were more than a few different aftermarket radio sets available plus the options offered by Ford.