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Question

An air column is constructed by fitting a movable piston in a long cylindrical tube. Longitudinal waves are sent in the tube by a tuning fork of frequency 416 Hz. How far from the open end should the piston be so that the air column in the tube may vibrate in its first overtone neglecting the end corrections?  
[ speed of sound in air =333 m/s ]
  1. 30 cm
  2. 45 cm
  3. 60 cm
  4. 90 cm


Solution

The correct option is C 60 cm
We know that for a closed organ pipe, the resonate frequency is given by,  
f=nv4l
For first overtone, n=3.
f=3v4l
416=3×3334×l
[overtone will be equal to the frequency of source] 
l=3×3334×416=0.60 m=60 cm

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