Two strings A and B have equal lengths and are made of the same material. String A has twice the diameter of string B. Both strings are stretched separately between identical rigid supports with the same tension.
a. (i) Obtain the ratio of the linear mass densities μA:μB of the two strings.
b. (ii) Deduce the ratio of their fundamental frequencies fA:fB.
c. (iii) If the fundamental frequency of string B is 400Hz, calculate the lowest frequency at which both strings can vibrate simultaneously without producing beats.