A Russian wave machine separately models the motion of a string of beads undergoing transverse and longitudinal wave motion. The mechanism of its operation is almost more interesting than the effect it demonstrates.
Longitudinal and transverse waves can also be separately demonstrated by the Space Phone [1] and the Rubber Hose [2]. A slinky can be used to demonstrate both also.
Links:
[1] https://demoweb.physics.ucla.edu/node/280
[2] https://demoweb.physics.ucla.edu/node/279