10.8.1 Displacement vs Pressure

Let’s recall that sound is a longitudinal wave, where the longitudinal oscillation of air particles produces regions of compression and rarefaction. As the sound wave travels, those regions of compression and rarefaction also get propagated along.

What do we get when two identical sound waves (same amplitude and frequency) travelling in opposite directions meet? A standing sound wave! What do the nodes and antinodes in a standing sound wave represent then?

If we are talking about pressure variation, then pressure nodes correspond to locations where the pressure remains constant at average pressure all the time, while pressure antinodes correspond to locations with maximum pressure variation (where the pressure alternates between the most extreme compression and rarefaction ).

We can also talk in terms of displacement variation, in which case displacement nodes correspond to locations where the air (as a medium) does not oscillate. On the other hand, displacement antinodes correspond to locations where the air (as an elastic medium) oscillate (longitudinally) with maximum amplitude.

One interesting thing to note is that the pressure nodes/antinodes are flipped with the displacement nodes/antinodes. In other words, a pressure node/antinode is a displacement antinode/node. Why?

Let’s look at the graphs below, which show the displacement and pressure envelope of a standing wave. Graphs are drawn in blue solid lines and red dashed lines to indicate the corresponding pairs in the two graphs.

Take the displacement node at position X for example: The displacement profile of the standing wave at this point alternates between \  (compression) and / (rarefaction). Basically, the air particles on either side of this point are always displaced in opposite directions. So they alternate between congregating towards this point and dispersing from this point. This causes a large variation in the pressure here, hence making this point a pressure antinode.

As for the displacement antinode at position Y: The displacement profile at this point is always flat —  (normal pressure). The air particles around this position are always displaced in the same direction and by the same amount. There is no change to the density of air particles here. The pressure remains constant at normal pressure, hence making this point a pressure node.

Applet

Walter Fendt (Standing Longitudinal Waves)

Concept Test

2067

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