Consider a block of mass $m$ attached to a spring. Let it oscillate at a frequency $f$. Now each part of the spring is in SHM. so this means a wave is propagating through this spring.bCan this wave be reflected at the fixed end of the spring resulting in the formation of standing waves?
Well, the reflection of a wave at the end happens always. One can picture this by imagining the succesive atoms being pushed off the equilibrium position as the wave propagates. Since the endpoint is fixed, it has nowhere to be pushed but the few atoms near it (I am considering idealized linear chain for simplicity) that have already being perturbed will, after having passed through equilibrium again, pass into the opposite direction.
For transversal waves (as those you have on strings of a guitar) this means that the wave perturbation will change from "up" to "down" at the end (and vice versa) while for the longitudinal waves (as those in your spring) there is a change from "compressed" to "streched" (and vice versa).