I am connecting my sound core with auxiliary cable to reduce blutooth , but sound core keep signaling because it's blue led is flashing all the time, so is it safe to use it beside my bed while being sleep to hear soft music?!
If you are concerned about Bluetooth radio frequencies as long as you don't sleep with it pressed up against your body you will be fine. Bluetooth is extremely low energy compared to Cellular networks and Wi-Fi.
Even if you ran it in Bluetooth mode it wouldn't be a big deal. The Soundcore is a receiver primarily after the initial pairing so there would be very little transmission radiation. The device you would be pumping into it from would be your main radiation generator.
What I mean when I connect aux does that disable the bluetooth or not? Is there way to disable bluetooth?
Connect it once via BT, then the light will stop flashing