Recently our pipes started a low groaning sound. It is almost rhythmic when water is on and sporatic when water if off. No temp changes but did have a new water pump installed in our 40 year old well about a month ago.

Did the noise start after the pump was installed? Check the tank levels on your toilet. The level should be one half inch under the top of the white overflow tube. Noise in your water system are caused by vibration. Sometimes this vibration is picked up by the rest of the system. We call this sympathetic vibration. I have found that most of weird noises can be tracked back to the toilets. Just giving you a place to start checking, let me know what you find. Good luck, Tom