Hello Ed, I am a retired electrical engineer 000s of volts and MWatts, with a strong envy for the small end of the scale and a self taught with such items as op amps. I have an old English sports car with soft top, which has a lot of road and exhaust noise in the cabin. I have not been successful with my efforts to develop a sound canceling system using one electret microphone in the boot with an amplifier and speakers separate from the radio in the cabin.
I wonder if you would share with me the schematic circuit of the amplifier you have developed ? David d.sparks21@ozemail.com.au

Hi Dave, ok the preamp I sue is not my design, I only changed a few values and added two more resistors to meet my needs. I will how ever point you to the website I got it from and share my changes. My changes make it less sensitive. The original design allowed it to pick up soft voice over 4 meters away and using it in a small hall as ambient mics gave me a lot of headaches. Check your email

 

Cars have mufflers that reduce the exhaust noise to nothing.
Yesterday I heard a loud noise and it was caused by a brand new Jaguar family car driven by a wealthy teen. It had its original muffler replaced by pipes that made more noise than with the muffler removed.

Some new cars have fake engine noise played though the sound system.

A sound can be cancelled by adding a similar sound of exactly the same frequency but with exactly the opposite phase.
It is difficult to add more than only one frequency and adjust its phase to cancel because the speed of sound is so slow that a small distance affects the phase. Then the phase of many sounds are all different due to distance.
Noise cancelling headphones have the microphone mounted directly on them so that the phase of most frequencies picked up by the microphone can be reversed to cancel the noise.