Wave propagation in 3D objects grows extremely complex beyond thin strings

Evidence

There are several different possible waves in three-dimensional objects. For example, there are different directions of vibration, and in addition there are different forms, depending on whether opposing surfaces are vibrating in similar or contrary motion, such as transverse, longitudinal torsional and others. As all of these different ways of moving will have different spring constants, they will be affected differently by external factors such as shape. This means that for any shape more complicated than a thin string, the velocity of propagation of transverse modes of vibration becomes extremely complicated. This becomes important when one considers the operation of percussion instruments. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 104

Categorization

• QUESTION: This hints that percussion instrument physics gets complicated in ways that might reward a dedicated deep dive.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 104