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 $13cm,41cm$ and $69cm$. The frequency of tuning fork, if velocity of sound is $350m{s}^{-1}$ 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 $40mm\frac{\lambda }{4}=1345mm\dots (i)$
and at second resonance $40mm\frac{3\lambda }{4}=4145mm\dots (ii)$
Subtracting Eq. (i) from Eq. (ii), we have
$30mm\frac{3\lambda }{4}-\frac{\lambda }{4}=41-13$
$\Rightarrow 30mm\frac{\lambda }{2}=28$
$\therefore 30mm\lambda =56cm$
Hence, frequency of tuning for $k$
$30mmn=\frac{v}{\lambda }=\frac{350}{56\times 10^{-2}}=625Hz$