A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end…

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 $13\text{ cm}$, $41\text{ cm}$ and $69\text{ cm}$. The frequency of tuning fork, if velocity of sound is $350\text{ ms}^{-1}$, is [DUMET 2011] A diagram showing a piston inside a cylindrical pipe pulled to the left, with a tuning fork placed near the open right end.
  1. 1250 Hz
  2. 625 Hz
  3. 417 Hz
  4. 715 Hz

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 $3\lambda / 4$.

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