Elastic waves are generated in a ferromagnetic material in a static magnetic field by a time-varying magnetic field which magnetostrictively couples to the material. We present modeling showing that this coupling is proportional not to the magnetostriction, but to the magnetization derivative of the static magnetostriction. We present experimental evidence showing that the elastic wave amplitude is a minimum (zero if no noise were present) at the field for which the magnetostriction derivative is zero and magnetostriction is maximum. No such minimum is found in steel when the field is high enough to make the magnetostriction go through zero and become negative. Thus, experiment also indicates that the coupling is proportional to the derivative of the magnetostriction, and not to the magnetostriction itself.