End Correction and Resonance

End Correction of the pipe

In organ pipes, the antinode actually lies a little outside the open end because the air just outside the open end is set into the vibration. So, the antinode displacement of the stationary wave occurs a little distance beyond the end.  Hence, the distance between the end point of the pipe and the position of antinode formed into the free end is called end correction of the pipe. It is denoted by x. For a closed pipe λ/4 = l +x and for an open pipe, λ/2 =l/2x.

Experimentally, it is found that the end correction of open organ pipe is 0.6D and that of closed organ pipe is 0.3D. Where D is the internal diameter of the tube.

Resonance

When a body is set into vibration, it vibrates with its own frequency called natural frequency. If an external force is applied on the body, then the body will vibrate with the frequency of the force applied on it. This vibration is called forced vibration. When the natural frequency of a body becomes equal to the frequency of the applied force, then the body begins to vibrate with very large amplitude and the body is said to be in resonance.  Resonance has significance role in our daily  life. The two important conditions for resonance to occur are given below:

  • The frequency of the applied force must be equal to the natural frequency of the system.
  • The applied force must be in phase with the vibrating system.

When a graph is plotted in between the amplitude of vibration and frequency of forced vibration, a curve is obtained as shown in figure.

Resonance of sound wave.

Here, a is the amplitude of vibration, f is the frequency of forced vibration is the fo is the resonant frequency.

 

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