To understand what is happening we need to look at the basics and work from there.
Density = Mass / Volume, so if the volume of a fixed mass of air increases, its density must decrease. If its volume decreases then its density must increase.
If we take a mass of air and warm it slowly, it will tend to expand. If the air is held within a container it will be unable to expand, so its pressure will increase. We will still have the same mass of air in the same volume, so the density will be unchanged. If we now reduce the volume of the container, the pressure, temperature and density of the air will all increase simultaneously.
If we now take the top off the container the air will be free to expand. As it expands it will take up a greater volume. We will now have the same mass of air in a greater volume, so the density will be lower. The pressure and temperature will also decrease as the air expands. So as the air expanded the pressure, temperature and density all decreased.
A shock wave is an instantaneous pressure increase. So when air flows through a shockwave it suddenly finds itself in an area of higher pressure. This causes the air to be instantaneously compressed until its pressure is equal to that immediately behind the shockwave. This sudden compression of the air causes its volume to decrease, so its density must increase. The sudden compression of the air also causes its temperature to increase. So we have a situation in which the pressure, temperature and density all increase simultaneously.
So passing the air through a shockwave causes it to behave as if it were inside a container which suddenly shrunk in volume.