Bluetooth Module and Amplifier on the same power supply

I'm using a Bluetooth Module and Amplifier module to play sound through my phone.

Bluetooth Module : http://www.dx.com/p/stereo-audio-bluetooth-speaker-module-blue-149203#.VY7ns_lVikp

Amplifier Board : http://www.dx.com/p/2-channel-3w-pam8403-audio-amplifier-board-red-146300#.VY7ntPlVikq

I've got the audio output of the Bluetooth module connected to the audio in of the amplifier board where speakers are attached. When these boards both have there interdependent power supply's the audio is very clear without noise.

When I power these modules both from the same power supply I get a humming and a lot of noise on the speakers.

I've looked into the concept of ground loops but struggle to apply it here. Can I power these boards from the same power supply? could someone explain why a group loop could be causing this problem?

It is not a ground loop it is lack of power supply decoupling.

Grumpy_Mike:
It is not a ground loop it is lack of power supply decoupling.

So I just need to use a capacitor? How large are we talking?

Maybe an inductor as well, you have to experement with the value but a 0.1 uF ceramic and something like a 47uF are a good starting point.