an aircraft flies at a constant power setting, straight and level in calm wind, airspeed = groundspeed = lets say 100kts.
Suddenly, the wind pick ups to a 40kt headwind.
Does the airspeed increase momentarily? Of course it does. The inertia of the aircraft will keep it moving at 100kts groundspeed and a higher airspeed will be observed for a moment (how high depends on how quickly the wind picked up), until the aircraft has slowed down to 60kts groundspeed, 100kts airspeed again.
For the same reason, you WILL see a momentarily increase of airspeed when turning into the wind and a decrease when turning downwind. It's not just perception, it works whether you look out the window or not.
If the inertia of the aircraft did not make a difference, why would the airspeed indicator jump all over the place when flying through turbulence?