Question

A piston filled 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 $350\, ms^{-1}$ is

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

Answer 1

Answer: (B)

625 Hz

Answer 2

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
$40\,mm \frac{\lambda}{4} = 13 45\,mm\, \dots (i)$
and at second resonance
$40\,mm \frac{3 \lambda}{4} = 41 45\,mm \dots (ii)$
Subtracting E (i) from E (ii), we have
$30\,mm \frac{3 \lambda}{4} - \frac{\lambda}{4} = 41 - 13$
$\Rightarrow 30\,mm \frac{\lambda}{2} = 28$
$\therefore 30\,mm \lambda = 56 \, cm$
Hence, frequency of tuning for $k$
$30\,mm n = \frac{v}{\lambda} = \frac{350}{56 \times 10^{-2}} = 625 \, Hz$