In general, jet engines on passenger aircraft make so much noise that in a long-duration flight it becomes really tiresome and uncomfortable. Nowadays, technology is much more advanced than before. Manufacturers have added many features to control the noise. Then, why do jet engines still produce so much noise?
Briefly: inside a jet engine's core or within its fan shroud, huge quantities of air get sucked through while their flow directions get rapidly changed up. This causes parcels of air to bounce off the walls of the engine passages and off their neighbors, a process that generates random (roaring) noise.
In addition, in the center of the engine's core, flammable fuel is continuously injected and vigorously mixed with air, and then set on fire. This too creates a roaring and hissing noise.
The compressor and turbine blades tend to shed sound waves as long as they are spinning around. For slow speeds (like a 2-bladed helicopter rotor, for example) each full rotation of the rotor sends two sound waves your way and you hear a whap-whap-whap noise. For lots of blades spinning at very high speeds, a screaming-siren noise is produced instead. On top of this, the fan on a high-bypass turbofan will emit a groaning moan when it comes up to full speed.
Then, at the exhaust port of the engine, the bypass, core, and ambient air flows get violently mixed which adds to the hiss and roar of the engine.
A turbine rotor fan spins at 10,000 RPM. With a diameter fan of 123 inches, it has a circumference (Pi x diameter) of 386 inches meaning it spins so fast on it's outer circumference it goes thru the air at 3,600+ miles per hour (Mach 4.8) , that's a huge amount air displacement and sound comes from air displacement