I have a newly installed ruud 13 seer heat pump, it works fine. It emits a constant hum,louder sometimes than others, this hum continues when machine is off, it will only cease when power is off to machine. I have heard various transformers sound similar,but should this heat pump make this constant hum?

Call your installer

Does this reply mean call my installer and report a problem,or call and ask if there is a problem?

Sorry, I didn't mean to give you such a short answer. I'd call the installer & report a problem. There shouldn't be any hum. If the sound is coming from the indoor section it's likely a transformer hum. Not a major problem but bothersome none the less & it shouldn't be there. If the noise is from the outdoor unit, the problem is likely a contactor. Easy to replace.