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 $350m/s$ , is

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

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