Two wires are kept tight between the same pair of supports. The tensions in the wires are in the ratio 2 : 1, the radii are in the ratio 3 : 1 and the densities are in the ratio 1 : 2. Find the ratio of their fundamental frequencies.

Sol. Frequency f = 1/ID √T/πp ⇒ f base 1 = 1/l base 1 D base 1√T base 1 πp base 1 ⇒ f base 2 1/ l base 2 n base 2√T base 2 πp base 2 Give that, T base 1/ T base 2 = 2, r base 1/ r bas 2 = 3 = D base 1/ D base 2 p bas 1/ r base 2 ½ so, f base 1/ f base 2 = l base 2 D base 2/ l base 1 D base 1 √T base 1/√T base 2√ πp base 2/ πp base1 (l base 1 = l base 2 = length of string) ⇒ f base 1 : f base 2 = 2 : 3