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  4. 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

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Q. 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 $350\, ms^{-1}$ isPhysics Question Image

Delhi UMET/DPMTDelhi UMET/DPMT 2006Electromagnetic Waves

Solution:

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 Eq. (i) from Eq. (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 $k$
$30\,mm n = \frac{v}{\lambda} = \frac{350}{56 \times 10^{-2}} = 625 \, Hz$

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