Q 11-14-039JEE MainJEE Main 2024 (1 Feb, Shift 1)Medium
A tuning fork resonates with a sonometer wire of length $1\ \text{m}$ stretched with a tension of $6\ \text{N}$. When the tension in the wire is changed to $54\ \text{N}$, the same tuning fork produces $12$ beats per second with it. The frequency of the tuning fork is ______ Hz.
Numerical value type. Enter your answer.
Answer: 6
The frequency of the wire is $f \propto \sqrt{T}$. At $6\ \text{N}$ the wire's frequency equals the fork frequency $f$.
At $54\ \text{N}$: $f' = f\sqrt{\dfrac{54}{6}} = 3f$.
Beats: $f' - f = 2f = 12 \Rightarrow f = 6\ \text{Hz}$.
Solution by Sreeraj P, M.Sc Physics