Question

A musical instrument is made using four different metal strings. 1, 2, 3 and 4 with mass per unit length μ, 2μ, 3μ and 4μ respectively. The instrument is played by vibrating the strings by varying the free length in between the range L₀ and 2L₀. It is found that in string-1 (μ) at free length L₀ and tension T0 the fundamental mode frequency is f₀.

List-I gives the above four strings while List-II lists the magnitude of some quantity.

List-I	List-II
(I) String-1 (μ)	(P) 1
(II) String-2 (2μ)	(Q) 1/2
(III) String-3 (3μ)	(S) 1/ 3
(IV) String-4 (4μ)	(T) 3/16
	(U) 1/16

If the tension in each string is T₀, the correct match for the highest fundamental frequency in f₀ units will be, 

(A) I → P, II → R, III → S, IV → Q

(B) I → Q, II → P, III → R, IV → T

(C) I → Q, II → S, III → R, IV → P

(D) I → P, II → Q, III → T, IV → S

Answer 1

Correct option (A) I → P, II → R, III → S, IV → Q

Explanation:

For all highest fundamental is when length is L₀