A tube of certain diameter and of length 48 cm is open at both ends. Its fundamental frequency of resonance is found to be 320 Hz. The velocity of sound in air is 320 m/s. One end of the tube is now closed, considering the effect of end correction, calculate the lowest frequency of resonance for the tube (in Hz).
The displacement curves of longitudinal waves in a tube open at both ends is shown in Figs. (a) and (b).
Let D be the diameter of the tube. We know that antinodes occur slightly outside the tube at a distance 0.3 D from the tube end.
In case of open organ pipe, the distance between two antinodes is
given by …(i)
We have,
Substituting the value of in Eq. (i), we get
In case of closed organ pipe,
Hence the lowest frequency is,
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An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at the both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is then n = ?
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