why do we not hear the supersonic jets when they approach us, but hear a sudden boom when they have gone away?

Sound Waves move in a elastic medium like air, water and ground and it is dependent on the temperature and humidity of the air the sound is traveling in and how fast sound will travel in that medium. Therefore a term called the sound barrier is considered which is considered as the speed at which sound is traveling. Therefore, if a supersonic aircraft moves beyond the speed of sound in air then it is said to go through the sound barrier and this is designated on the ground as a sonic boom. If you are standing on the ground as the supersonic aircraft passes by then there will be a short time delay and then you will hear the boom which is the sonic boom which is merely a loud noise that results from the high pressure sound followed by a low pressure sound.