Given below are some examples of wave motion. State in each case if the wave motion is transverse,longitudinal or a combination of both:
$(a)$ Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.
$(b)$ Waves produced in a cylinder containing a liquid by moving its piston back and forth.
$(c)$ Waves produced by a motorboat sailing in water.
$(d)$ Ultrasonic waves in air produced by a vibrating quartz crystal.

(N/A) Transverse and longitudinal: The sideways displacement creates a transverse component,while the spring's inherent nature allows for longitudinal propagation.
$(b)$ Longitudinal: The back-and-forth motion of the piston creates pressure variations in the liquid,which travel as longitudinal waves.
$(c)$ Transverse and longitudinal: $A$ motorboat creates surface ripples (transverse) and pressure disturbances (longitudinal) in the water.
$(d)$ Longitudinal: Sound waves,including ultrasonic waves,travel in air as pressure variations,which are strictly longitudinal.