A musical instrument is made using four different metal strings 1, 2, 3 and 4 with…

PHYSICS · Single correct · CBSE · Physics · Waves · Waves

Problem

A musical instrument is made using four different metal strings 1, 2, 3 and 4 with mass per unit length μ\mu, 2μ2\mu, 3μ3\mu and 4μ4\mu respectively. The instrument is played by vibrating the strings by varying the free length in between the range L0L_0 and 2L02L_0. It is found that in string-1 (μ\mu) at free length L0L_0 and tension T0T_0 the fundamental mode frequency is f0f_0. List-I gives the above four strings while list-II lists the magnitude of some quantity. [Adv. 2019]
List-IList-II
(I) String-1 (μ\mu)(P) 1
(II) String-2 (2μ2\mu)(Q) 1/2
(III) String-3 (3μ3\mu)(R) 1/21/\sqrt{2}
(IV) String-4 (4μ4\mu)(S) 1/31/\sqrt{3}
(T) 3/16
(U) 1/16
If the tension in each string is T0T_0, the correct match for the highest fundamental frequency in f0f_0 units will be, (1) I→Q,II→P,III→R,IV→TI \to Q, II \to P, III \to R, IV \to T (2) I→Q,II→S,III→R,IV→PI \to Q, II \to S, III \to R, IV \to P (3) I→P,II→R,III→S,IV→QI \to P, II \to R, III \to S, IV \to Q (4) I→P,II→Q,III→T,IV→SI \to P, II \to Q, III \to T, IV \to S

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