Place a ping pong ball in a water bath. Drop one drop of water in the bath and describe the motion of the ball. Is the wave motion transverse or longitudinal?

Its wave motion is transverse.

Explanation:

On the surface of water whenever a mass is dropped leading to a periodic oscillation of the surface molecules form a transverse wave on the surface of the water i. e. the oscillations occur in a direction perpendicular to the direction of propagation of waves.

In the case of a longitudinal wave, the direction of propagation is parallel to the direction of oscillations.

On the surface of the water, the patterns of disturbance are formed due to the surface tension of the water.