Pro-97
I own several PRO-97s. When using an AC adapter, and the backlight is on, one of the PRO-97s has a "hum" in the audio. If I run it from batteries, it goes away. If I turn off the backlight it goes away. The same AC adapter does not cause this problem on other PRO-97s or PRO-95s. Every AC adapter I have causes this problem only on this scanner. Also, it does not matter which batteries I am using, or their level of charge; although a higher charged set of batteries reduces the hum.
In my case I am fairly certain there is a filter cap which is not up to spec or a coil shorted. It is not significant enough for me to trace it out and fix it. It sounds like you're hearing the same thing. And with headphones that hum has to be very clear.