Is the boombox using a Logitech "unity" wireless receiver dongle plugged into a USB 3.0 port?
Especially if plugged into a USB 3.0 hub, expect RF interference to reduce range due to USB 3.0 spread spectrum properties.
Basically, USB 3.0 can generate lots of 2.4 GHz radio noise that interferes with other devices in that frequency band, reducing their range.
It is definately an issue in the laptops introduced earlier this year, as the first USB 3.0 from Apple. But this is the first indication I've seen that it wasn't fixed for the new iMacs (I'm assuming this is a late-2012 model...)
But if the Logitec receiver is plugged into a hub, it could be the hub that's leaking noise. Try disconnecting the hub and plugging directly into the iMac USB 3.0 ports and see if that helps.