The phenomena of generating sound by blowing into a tube is an example of resonance. In resonance, a system that has a natural frequency is excited by an oscillation of the same frequency. A familiar example is pushing a child on a swing. The swing is a pendulum, with a single natural frequency. When the child is pushed so that the push is in the same direction as the child’s velocity, energy feeds into the system rapidly and the child swings higher and higher (the system here is the child on the swing). If the push is opposed to the child’s velocity, energy drains out of the system rapidly.

Sound, too, can be pictured as a regular series of pushes and pulls. The sound wave is compressional, so the wave is a pattern of regular pressure changes.

One important difference between blowing into a tube and pushing a child on a swing is that the push is made at just the right time to get the child swinging with large amplitude. The push has a single frequency. By contrast, the sound of blowing into a tube is noise—a random spectrum of unrelated frequencies. But when that spectrum contains a frequency that makes the tube resonate, then the sound level in the tube builds up and up. Listening to a sea shell is the same effect. Now imagine a tube, with length “L,” that is closed at one end. A sound wave reaches the open end of the tube. The wave moves to the end of the tube, reflects, and returns to the open end, which requires a time of 2L/v, as shown.

When the wave returns to the open end, the wave will be pushing the air at this end out of the tube. For resonance to occur, the sound wave exciting the tube must have gone through a half a cycle since it entered the tube, which requires a time of half the period T.

2L/v = T/2 = 1/(2f)
Substituting v = Λ X f gives
L = Λ/4
This equation expresses the same result as the drawing on page 203 in the Student Book.