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So, I'm concluding that the important content for an introductory cal-based course, regarding modes of wave motion is there are 3 primary modes of mechanical wave propagation: transverse, longitudinal, and torsional. Actual waves are very complicated and can be sums of these three modes as well as sums of many frequencies of simple harmonic waves. Understanding the basic properties of wave motion (amplitude/intensity, period/frequency, wavelength, wave speed) apply to all these modes, but the speeds of each mode, even in a common structure will differ, and the strength of the material of the structure will differ for each mode.