$A$ medium can carry a longitudinal wave because it has the property of

The angle between the particle velocity and wave velocity in a transverse wave is [except when the particle passes through the mean position].

Transverse and longitudinal waves can propagate in solids,whereas only longitudinal waves can propagate in air. Explain this statement.

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.

To propagate both longitudinal and transverse waves,a material must have

$Assertion :$ When a beetle moves along the sand within a few tens of centimeters of a sand scorpion,the scorpion immediately turns towards the beetle and dashes towards it.
$Reason :$ When a beetle disturbs the sand,it sends pulses along the sand's surface. One set of pulses is longitudinal while the other set is transverse.