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Q.

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.

 COLUMN -I  COLUMN-II
I)string -1 (μ)   P)1
II)String – 2  (2μ)Q)1/2
III)String - 3 (3μ)R)1/2
IV)String - 4 (4μ)S)1/3
  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 

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a

IP,IIQ,IIIT,IVS

b

IQ,IIP,IIIR,IVT

c

IP,IIR,IIIS,IVQ

d

IQ,IIS,IIIR,IVP

answer is C.

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Detailed Solution

For string 1:  f0=12L0T0μ
For string 2:  f=12L0T02μ=f02
For string 3:  f=12L0T03μ=f03
For string 4:  f=12L0T04μ=f02
 

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