That said, hand and wrist x-rays are a standard use as a predictor of skeletal maturity in children, so it may be that your son has finished growing. The growth plates in the knees generally close at about the same time as the ones in the wrist. The usual progression of fusion of growth plates is elbow first, then foot and ankle, then hand and wrist, then knee, then hip and pelvis, and last the shoulder and clavicle. It is possible that he has finished, however 14 would be quite early for a boy to stop growing, unless he has gone through puberty early. Most boys don't stop growing until about age 17.
The main factor that determines when the growth plates fuse is the rise in various hormones that takes place with puberty. Testosterone, which is the major hormone in boys, promotes growth as well as maturation of bone, eventually causing the growth plates to fuse. For boys, the growth spurt occurs fairly late in puberty, after there is already a fair amount of pubic hair and the penis and testes have enlarged to almost their full size. If your son is more in the middle of puberty, it is likely that he still has some growth in height left, in spite of a wrist that is no longer growing. If your son has already gone completely through puberty, it is more likely that he has finished growing. Your son's doctor can assess this more at his next visit.