JEE (Advanced) 2019 Paper-2 Question 16

Instructions

A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $$\mu, 2\mu, 3\mu$$ and $$4\mu$$ respectively. The instrument is played by vibrating the strings 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.

Question 16

The length of the strings 1, 2, 3 and 4 are kept fixed at $$L_0, \frac{3L_0}{2}, \frac{5L_0}{4}$$ and $$\frac{7L_0}{4}$$, respectively. Strings 1, 2, 3, and 4 are vibrated at their $$1^{st}, 3^{rd}, 5^{th}$$ and $$14^{th}$$ 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,



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