Q 11-14-079JEE MainJEE Main 2022 (27 Jul, Shift 2)Easy
A wire of length $30$ cm, stretched between rigid supports, has it's $n^{\text{th}}$ and $(n + 1)^{\text{th}}$ harmonics at $400$ Hz and $450$ Hz, respectively. If tension in the string is $2700$ N, it's linear mass density is ______ $\text{kg m}^{-1}$.
Numerical value type. Enter your answer.
Answer: 3
Successive harmonics differ by the fundamental:
$$\frac{v}{2L} = 450 - 400 = 50 \Rightarrow v = 50\times2\times0.3 = 30\ \text{m s}^{-1}$$
$$\mu = \frac{T}{v^2} = \frac{2700}{900} = 3\ \text{kg m}^{-1}$$
Solution by Sreeraj P, M.Sc Physics