Q 11-14-131JEE MainJEE Main 2018 (15 Apr, Shift 1)Medium
A tuning fork vibrates with frequency $256\ \text{Hz}$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (speed of sound in air is $340\ \text{m s}^{-1}$)
Answer: (B) $200\ \text{cm}$
With 1 beat per second, the pipe's frequency is $255\ \text{Hz}$ or $257\ \text{Hz}$.
The third normal mode of an open pipe has
$$f_3 = \frac{3v}{2L} \quad\Rightarrow\quad L = \frac{3v}{2f_3}$$
For $f_3 = 255\ \text{Hz}$:
$$L = \frac{3\times340}{2\times255} = 2.00\ \text{m} = 200\ \text{cm}$$
($f_3 = 257\ \text{Hz}$ gives $198.4\ \text{cm}$, which is not an option.)
Solution by Sreeraj P, M.Sc Physics