A steel guitar string has a tension T, 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 decreased by a factor of 3. The diameter is D and the length is L.
(b) The diameter of the string is increased by a factor of 2. The tension is T and the length is L.
(c) The length of the string is decreased by a factor of 2. The tension is T and the diameter is D.