Chapter 11, Problem 10Q

What kind of waves do you think will travel along a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its length?

To determine

What kind of waves do you think will travel along a horizontal metal rod if you strike its end vertically from above and horizontally parallel to its length.

Answer to Problem 10Q

Solution:

Transverse waves, Longitudinal waves

Explanation of Solution

Striking a horizontal metal rod vertically from above is going to deflect the struck area downward. Inertia will prevent the entire rod from reacting downward at the same instant so the rod will be flexed with the struck point being low. The springiness of the rod will tend to straighten it but overshoot the initial straight condition, causing the struck area to go high relative to the rest of the rod. As you suggest you will end up with an up and down movement of the particles making up the rod. Depending on the length, stiffness and mass of the rod there may be one or more nodes along the rod's length where there is essentially no motion in the vertical direction while the rod on either side of these nodes move up and down.

That may not be the whole story, depending on the level of detail you look at. The up and down flexing motion in the rod is not totally isolated from motion along the rod's length. In real materials there is coupling between modes of oscillation so that some of the energy imparted to the rod will end up producing a longitudinal compression wave in the rod, essentially sound waves, running along the rod and reflecting from the ends. These waves involve motion of the rod's atoms back and forth horizontally.

Striking it horizontally on its end should cause a longitudinal wave through the rod. Striking it vertically on its end should cause a transverse wave along the rod. The two waves are quite different so their wave velocities will be quite different and, therefore, their resonant frequencies will be quite different. That is, the sound produced will be quite different.Transverse waves oscillate at right angles to the direction of wave travel, while longitudinal waves oscillate in the direction of travel.