An object has undergone acceleration if ...
-- it's moving faster than it was before
or
-- it's moving slower than it was before
or
-- it's moving in a different direction that it was before.
There are longitudinal and transverse. Both types of mechanical waves require a medium, transport energy, and have defined wavelengths, frequencies, and speeds.
Differences are that transverse waves oscillate along a direction perpendicular to the direction of travel (like shaking a rope up and down). Longitudinal waves like oscillations along a spring and sound waves, oscillate back and forth along the direction of travel.
