A musical instrument is made using four different metal strings. 1, 2, 3 and 4 with mass per unit length `mu,2mu,3mu and 4mu` respectively. The instrument is played by vibrating the string by varying the free length in between the range `L_(0) and 2L_(0)`. it is found that in string-1`(mu)`. at free length `L_(0)` and tension `T_(0)` the fundamental mode frequency is `f_(0)`. List I gives the above four strings while list-II lists the magnitude of some quantity.


Q. The length of the strings 1, 2, 3 and 4 are kept fixed at `L_(0),(3L_(0))/(4), and (7L_(0))/(4)`, respectively. Strings 1 2, 3, and 4 are vibrated at their 1st 3rd, 5th, and 14th harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of `T_(0)` will be:

Options

A. `ItoQ,IItoS,IIItoR,IVtoP`
B. `ItoP,IItoR,IIItoS,IVtoQ`
C. `ItoP,IItoQ,IIItoT,IVtoS`
D. `ItoQ,IItoP,IIItoR,IVtoT`

Answer

B

Explanation

To keep fundamental frequency higher
`fo_1=(1)/(2L_0)sqrt((T_0)/(mu))=fo, fo_2=1/(3L_0)sqrt((T_0)/(2mu))=(fo)/(sqrt2)`
`fo_3=1/(2L_0)sqrt((T_0)/(3mu))=(fo)/(sqrt3), fo_4=1/(2L_0)sqrt((T_0)/(4mu))=(fo)/(sqrt4)=f_0/2`