How did Andrija Mohorovicic discover the moho?
Mohorovicic discovered the crust-mantle boundary, which now bears his name, by studying seismic waves.
In this answer (https://socratic.org/questions/how-was-mohorovicic-discontinuity-discovered) by @Suryin=) it is noted that Mohorovicic discovered the crust-mantle boundary by noting a change in speed of the seismic waves.
Specifically, as one crosses the boundary the predominant mineral composition of the rock changes, and the minerals on the mantle side enable seismic waves to travel faster. The faster speed of waves that go deeper into the Earth is what Mohorovicic observed.