Why do helicopters make the pulsing noise when they fly

Time to cut to the chase. The sound or pitch is produced by the number of blades 2-ship or 4-ship as an example. The pulse u hear is the blade passing over the tail section. The air is being pushed down & contacts the aft section causing the pulse or thump as we used to call it. You can tell by the number of blades what type of helicopter it is. The same make & model helicopter will make a different sound pulse depending on the type of blade installed. Some blades r wider used for heavy lift vs the narrow blades the sound is different. The balde slip is the caused by the retreating blade traveling faster than the approaching blade. The faster the blades flies the more lift it creates lifting the blade up until it hits its stop.

The blades on a helicopter travel at different speeds as they rotate around the hub. All of this will change the pitch as it passer over the tail section. This is where the terms lead & lag come from.

The rotor blades r wings & they do not cut the air (choppers). This is why they r called rotor wing.

I've read that the sound is a result of the tips of the rotor blades going supersonic.

If u can imagine a spinning rotor blade, the part near the hub or attachment point is moving slow when compared to the tip. This pop, pop, pop, sound u hear as a helicopter is coming toward u is these small sonic booms from the rotor tips.

Notice how as the chopper gets close & the craft passes over head the noise stops. This is because of the forward speed of the vehicle & other factors. The sound is still there but someone else is hearing it.

When a helicopter blade sweeps around forward it is turned at an angle to produce greater lift. (like when u stick ur hand out of a moving car & then turn it) As that same blade comes back around the rear of the helicopter it is turned to a horizontal position. The blade is shaped like an airplane wing & the rearward swing also produces lift but not as much as the blade achieved when it was sweeping forward.
The greater lift in the front is what causes the craft to go forward.

It is called the Acoustical signature, aka blade slap.
On a 2 bladed system (a Bell 204/205 is a very good example) it is very pronounced especially at 60kts and about a 500 fpm decent.

The loud ''thump thump thump'' noise you sometimes hear from helicopters is called ''blade slap.'' It is generally caused by poor piloting technique and we try to minimize it as much as possible since it annoys people on the ground. Blade slap occurs when the helicopter is allowed to slowly drift downward while the pilot is still pulling significant power. When blade slap occurs, the pilot should either stop the descent, or lower the collective to enter a more positive descent.

The noise is generated by the rotor blades of the helicopter, which generate the helicopter is lift. The rotors generate a sort of wind noise, and each time the rotor swings closer or further from an observer doppler effect causes a change in the volume of the sound heard.

The rotor blades are breaking the speed of sound or are very close to it and that is the thumping sound you here.

That noise because of the big rotor hitting / cutting the air. It chops chops and hence the name chopper.

Rotors.