Chapter 15.2, Problem 19PP

To determine

To Find: The relation between the length of the open tube and the wavelength of the sound to produce the strongest resonance.

Answer to Problem 19PP

  $L=\frac{\lambda }{2}$

Explanation of Solution

Introduction:

A pipe that is open from both the ends is known as open pipe. The strongest resonance in the open pipe takes place at the first resonance, second resonance and so on.

Wavelength is defined as the distance between the two consecutive crests or trough. It is denoted by the symbol $\lambda$ .

Resonance is defined as the process of increasing the amplitude which takes place when the periodically applied force frequency matches with the natural frequency on which it acts.

Consider an open pipe having length $L$ . The sound wave is vibrating with one node and two antinodes.

Separation between the two consecutive antinodes can be given as:

  $L=\frac{\lambda }{2}$

Where,

  $\lambda$ is the wavelength.

Conclusion:

Hence, the relation between the wavelength and the length of the pipe is $L=\frac{\lambda }{2}$