Q 11-14-132JEE MainJEE Main 2018 (15 Apr, Shift 2)Medium
5 beats/second are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either $0.95\ \text{m}$ or $1\ \text{m}$. The frequency of the fork will be:
Answer: (A) $195\ \text{Hz}$
For a sonometer wire, $f \propto \dfrac1L$, so the $0.95\ \text{m}$ length has the higher frequency. With the fork frequency $f$:
$$f_{0.95} = f + 5, \qquad f_{1} = f - 5$$
$$\frac{f + 5}{f - 5} = \frac{1}{0.95} \quad\Rightarrow\quad 0.95f + 4.75 = f - 5 \quad\Rightarrow\quad f = 195\ \text{Hz}$$
Solution by Sreeraj P, M.Sc Physics