Question

A piston fitted in cylindrical pipe is pulled as shown in the figure. $ A $ tuning fork is sounded at open end and loudest sound is heard at open length $ 13 $ cm, $ 41 $ cm and $ 69 $ cm, the frequency of tuning fork if velocity of sound is $ 350 \,m/s $ , is

• A. $ 1250\,Hz $
• B. $ 625\,Hz $
• C. $ 417 \,Hz $
• D. $ 715\,Hz $

Answer 1

Answer: (B)

In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at $\lambda /4$ and second resonance occurs at $ 3\lambda / 4$.

Thus,at first resonance
$\frac{λ}{4} = 13 \quad ...(i)$
and at second resonance
$\frac{3λ}{4} = 41 \quad ...(ii) $
Subtracting Eq. $(i)$ from Eq. $(ii)$, we have $\frac{3λ}{4} - \frac{λ}{4} = 41 − 13 $
$⇒ \frac{ λ}{2} = 28$
$∴ λ = 56 \,cm$
Hence,frequency of tuning fork
$n=\frac{v}{\lambda}=\frac{350}{56 \times 10^{-2}}=625 Hz$