Our cold water pressure pulses with a reliable pattern of pulsing for about 10 seconds every minute and has been going on for about 5 months getting progressively worse. We've had our city water department come check the water lines and they couldn't find an issue. We do not have a check valve on the main nor is there a meter. This issue does not occur with the hot water and we can not find evidence of any leaks. We have not made any changes or additions to appliances or water lines in the last 5 years either. Besides a possibility of a poltergeist (sorry that's all I can think it is at this point) what can be causing this pulsating pressure?

Observe the meter next time the sound occurs to see if the flow indicator is turning.

we do not have a meter as stated in the original message. no meter, no check valve. it's a direct service from the city's water main.

If you do not have a pressure regulating valve, then the only option is to install a pressure gauge and see what is happening when it pulsating. If YOU do not have any devices, such as a water softener, that could cause it then it may be a city problem, regardless of what they are telling you.

the city already used a pressure gauge to check the fluctuations (see original message). They could see the pulsating pressure changes but said it wasn't at the main it was something INSIDE causing it.... Hence the original question of WHAT COULD CAUSE THIS.

Put a pressure gauge on the system, then shut the main, and see if the pressure drops off.

And YOU "believed" them? Nothing you have told gives us any idea if there is ANYTHING inside your house to cause the noise.