The information from the Physical encyclopedia of 1992
about the cylindrical magnetostriction oscillators.

At big desire we can use for creation of a cylindrical oscillator the design, similar represented on figure, which here I outlined  by a red marker. Only we should remember, that according to our needs the sound waves will radiates inward of the cylinder, therefore loops of the electric wires covering walls of the cylindrical core of a oscillator, we should place outside. Besides it will be necessary to provide an additional wire, which make magnetic biasing of the cylindrical core.