12.5 Sound interference and resonance: standing waves in air columns  (Page 5/11)

We have emphasized sound applications in our discussions of resonance and standing waves, but these ideas apply to any system that has wave characteristics. Vibrating strings, for example, are actually resonating and have fundamentals and overtones similar to those for air columns. More subtle are the resonances in atoms due to the wave character of their electrons. Their orbitals can be viewed as standing waves, which have a fundamental (ground state) and overtones (excited states). It is fascinating that wave characteristics apply to such a wide range of physical systems.

Phet explorations: sound

This simulation lets you see sound waves. Adjust the frequency or volume and you can see and hear how the wave changes. Move the listener around and hear what she hears.

Section summary

• Sound interference and resonance have the same properties as defined for all waves.
• In air columns, the lowest-frequency resonance is called the fundamental, whereas all higher resonant frequencies are called overtones. Collectively, they are called harmonics.
• The resonant frequencies of a tube closed at one end are:
  $f_n=n\frac{v_{\mathrm{w}}}{4L}\text{, }n=\mathrm{1,\; 3,\; 5}\text{.}\text{.}\text{.,}$
  $f_1$ is the fundamental and $L$ is the length of the tube.
• The resonant frequencies of a tube open at both ends are:
  $f_n=n\frac{v_{\mathrm{w}}}{2L}\text{, }n=\mathrm{1,\; 2,\; 3}\text{.}\text{.}\text{.}$

Conceptual questions

Problems&Exercises