Creating musical sounds
Creating musical sounds

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Creating musical sounds

5.7 Vibrating air column: reflection at the end of an air column

When a sound wave reaches the end of an air column, it is clear that it will be reflected if the tube end is closed. You only have to imagine yourself standing some distance, let's say 50 metres, away from a flat wall. If you shout, you will hear an echo – the reflection of the sound wave you projected.

There is one difference, though, between the reflection of a sound wave and the reflection of the wave on a string that you met previously. When a sound wave is reflected from a closed end, it is not inverted. In other words, a compression (a high-pressure region) in the incident wave will return as a compression in the reflected wave. Similarly, a rarefaction (a low-pressure region) in the incident wave will return as a rarefaction in the reflected wave. Figure 12 shows one cycle of a sinusoidal pressure wave travelling down an air column and being reflected at a closed end. In the incident wave, a compression leads a rarefaction. Upon reflection, there is no inversion: the compression still leads the rarefaction in the reflected wave. (In Figure 12, the pressure variation is represented both graphically and in terms of the separation of the air molecules.)

You may be surprised to learn that a sound wave is also reflected when it reaches an open end of a tube. In practice, it will be only partially reflected. There must be some wave energy transmitted from the end of the air column otherwise wind instruments, for example, wouldn't produce any sound when blown! However, the amount of wave energy that is emitted by a wind instrument is surprisingly small, being only around 1% of the energy possessed by the vibrating air column. But why should the sound wave be largely reflected back up the air column? Surely upon reaching the open end of the tube it should just continue into the outside world.

To help explain why there is reflection, consider a rarefaction propagating along an air column towards an open end. The open end is at atmospheric pressure. When the rarefaction reaches the open end, the pressure there is suddenly reduced. Air molecules are sucked into this partial vacuum from the outside world and the pressure at the open end is restored to atmospheric pressure. However, the air molecules that are sucked into the tube have inertia. They don't just suddenly stop at the open end; instead, they continue moving into the tube and squeeze against the air molecules already residing there. A compression is created, which propagates back down the air column away from the open end.

Figure 12
Figure 12 One cycle of a sinusoidal pressure wave (e.g. a sound wave): (a) approaching the closed end of an air column; (b) returning after reflection from the closed end
Figure 13
Figure 13 One cycle of a sinusoidal pressure wave (e.g. a sound wave): (a) approaching the open end of an air column; (b) returning after reflection from the open end

You may have noticed from this explanation that when a sound wave reaches the open end of a tube, not only is it reflected but it is also inverted. A rarefaction in the incident wave becomes a compression in the reflected wave. Similarly, a compression in the incident wave becomes a rarefaction in the reflected wave. Figure 13 shows one cycle of a sinusoidal pressure wave travelling down an air column and being reflected at the open end. In the incident wave, a compression leads a rarefaction. In this case, when the wave is reflected it is also inverted. As a result, in the reflected wave, it is a rarefaction that leads a compression.

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