We infer that crickets and katydids in the distant past communicated with sound based on the presence of sound receptor organs (ears) on fossils. The other evidence of sound communication by crickets and katydids comes from fossils that contain the sound production mechanism.
Modern katydids produce sounds by rubbing their wings together. The wings are asymmetric; One wing contains a series of teeth, the other wing contains a plectrum (or scraper). Sound is produced when the plectrum rubs across the teeth, causing the teeth to vibrate. The vibration in the teeth is transferred to the air (sound is vibrating air).
A recent paper in PNAS analyses a katydid fossil from 165 million years ago that has the sound producing mechanism on the wings remarkably preserved. This fossil is called Archaboilus musicus, to emphasize its singing ability. The pitch of the sound is a function of the mechanical properties of the teeth. From the available evidence, it is inferred that Archaboilus musicus produced a single tone song with a pitch that is much lower than most of extant katydids and tree crickets.
Careful analysis of ancient fossils tell us that the Jurassic Forests were filled with the sounds of calling insects, although the sounds would have a different character from our familiar forests.