Understanding Beats: The Interplay of Air Pressure in Sound Waves

[mrhingle]

What would happen if an air pressure increase from one sound wave were located at the same place and time as a pressure decrease from another of the same amplitude?

 

[PeterO]

What would happen if an air pressure increase from one sound wave were located at the same place and time as a pressure decrease from another of the same amplitude?

In brief - there would be no change in the air pressure.

This is the situation we find at the nodes for standing waves occurring inside all long, thin tubes moulded as musical instruments: ie Flutes, trumpets, oboes, bassoons, Tubas, Bugles, Clarinets, Pipe organs, etc.

You will get the same event if you get two loud speakers, place them several meters apart, facing each other preferably, and connect them to a signal generator producing a single sine wave. If you stand between the speakers and move towards one of the speakers, you will notice points of little or no sound, between points of considerable sound.
The effect is most notable near the mid point of the speakers [have a think about why].
It is also best to be facing a speaker, so that the line connecting your ears is perpendicular to the line connecting the speakers; other wise your ears may go quiet alternately and you will not notice the very quiet points.

You could alternately place those two speakers a few metres apart at one end of a sports field, facing out, then move 20-30m down field directly in front of the speakers. Then move transversely across the field and you will again notice loud and quiet points. The quiet points are ones which are like the places you described.

 

[PeterO]

What would happen if an air pressure increase from one sound wave were located at the same place and time as a pressure decrease from another of the same amplitude?

Don't forget that an air pressure increase from one sound wave will be followed very shortly by a pressure decrease from that sound wave.
If the frequency of the second sound wave is a match for the first, then the pressure decrease from that second wave will be similarly followed by a pressure increase, and the cancellation will be continuous.
If the frequencies are different you will get fluctuations between "no variation in pressure" and "maximal variation in pressure". You will experience what we call "beats". When an orchestra tunes up, they are ensuring that beats do not occur. You also do that when you tune a guitar [unless you are using one of those little electronic tuning devices].