Method of propogation of mechanical waves

Question

My textbook has a chapter on Waves, focusing specifically on Mechanical ones. It says the following statement for the Transverse and Longitudinal waves.

Transverse waves only travel in a medium which opposes tensile force while longitudinal waves travel in mediums which can exert an opposing compressive force.

The book doesn't state any examples for the above statement, which confuses me. I know the basics of how waves travel, but why is opposing tensile force and compressive force necessary? I think there is some gap between what the book wants to convey and what I am understanding at my level. Any help will be greatly appreciated. If you could suggest some text for background reading, it would be even more helpful. Thanks a lot in advance!

Answer 1

The statement is poorly articulated. A more accurate statement would be "Transverse waves travel only in media with a nonzero shear modulus, whereas longitudinal waves can travel in any medium with a nonzero bulk modulus (which is every stable material)."

Since ideal fluids have no shear stiffness, no mechanism exists that can carry transverse vibration through them. (Put another way, there's no finite S-wave velocity.)

However, all stable materials resist confined compression (i.e., they have a nonzero bulk modulus, which contributes to the longitudinal modulus), and so there is a meaningful P-wave velocity.

(Possibly the author is trying to say that traverse waves can propagate only in materials with a nonzero unconfined, uniaxial tensile strength, which does exclude fluids because their Young modulus is zero. However, the statement emerges as very confused because the nuances of tensile and compressive resistance are omitted.)

Is the revised statement consistent with your understanding of traveling waves?