Standing waves in instruments

Recall that we considered earlier the case of standing waves on a string:

• Viewgraph 0

  Today, let's focus on a different type of standing wave: the pressure wave in a column of air.

• Viewgraph 1

• Viewgraph 2

  Take a look at the nice illustration of standing waves in a tube created by Daniel A. Russell.

• Viewgraph 3

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• Viewgraph 6

• Viewgraph 7

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  Consider the western flute, which is (in very simple terms) a tube open at both ends.

  1. The flute in the picture above has a total length of about L = 100 cm. What should the fundamental frequency of a flute be?

  But flautists can produce much higher frequencies! How? By opening one or more holes in the body of the tube.

  2. The flute has one hole at a distance 50 cm from the end of the tube. If that hole were opened, what would the frequency be?

  But flautists can STILL produce higher frequencies! How? By opening two or more holes.

  3. Suppose the flautist opens two holes which are 40 cm and 45 cm from the mouth end of the tube. What frequency would resonate now?

• This Fourier Synthesis applet lets you create a waveform by adding sines and cosines, then listen to it.