A steel guitar string has a tension F, length L, and diameter D. Give the multiplicative factor by which the fundamental frequency of the string changes under the following conditions:
(a) The tension in the string is increased by a factor of 4. The diameter is D and the length is L.
(b) The diameter of the string is increased by a factor of 3. The tension is F and the length is L.
(c) The length of the string is halved. The tension is F and the diameter is D.