Air compressors are loud, there's no way around it. While some models are quieter than others are, they all create noise while running. It is impossible to make an air compressor 100% noise-free, but there are a few things you can do to reduce the noise to a more bearable level, and protect your hearing.
Wear hearing protection when using air compressor
The most important thing to do is wear hearing protection when using an air compressor. The noise emitted from an air compressor is loud enough to cause permanent hearing loss over time. Hearing protection doesn’t reduce the noise the air compressor makes, but it will reduce the noise you hear.
Location of air compressor for noise reduction
Locate the air compressor as far away from the work area as possible, or in a corner of the shop or garage. Try building an enclosure for the air compressor using materials that absorb noise. Be sure to consider airflow, allowing for both air intake and for cooling. Never completely cover or enclose an air compressor, as this will cause serious overheating.
Install a muffler or silencer on the air compressor
Most of the noise generated comes for the intake side of the pump. There are inlet filter/silencers–or mufflers–available that can reduce noise at differing degrees. It may help to install a 90-degree elbow on the air intake, and then install a silencer.