Wireless speakers. can I buy a cd radio hi fi system that can transmit to a wireless speaker in the bedroom from the lounge?

The latest Bose Wave Sound Touch will do that...Also you could get a Denon AV receiver with Heos and then attach a CD player to the receiver and transmit to other Heos speakers through out the house...I think Yamaha has a similar system called Music Cast that will also do that in a similar fashion....The advantage with Heos is you can also use other compatible Play Fi speakers by Wren ; Phorus; Omni and others it doesn't have to be just Denon Heos speakers....

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They don't make a hifi stereo that transmits. Get a wireless transmitter like bluetooth to transmit from the stereo to the bluetooth wireless speaker. Those are very short range though- only about 30 feet. Better to run wires from the lounge to the bedroom and connect speakers that way.

Sure. What you are describing is technology that has been around since the 1980's.

I checked Amazon for some products.

You basically just need to get a cd player as part of a hifi system (which are actually a bit hard to come by these days) that can connect up to a wireless transmitter and speaker.

You can get something like this -- a DPNAO Portable cd Player，Boombox, with Headphones Jack FM Radio Clock USB SD and Aux. (I do not want to provide a link here, just search for it).

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Then what you would do is buy something like this (not bluetooth which requires that your speaker and cd radio have to be in visual site with each other) a portable speaker with transmitter that would go into into the aux output of the boombox or hifi system: Acoustic Research AWS63S Mainstreet Indoor/Outdoor Portable Wireless Speaker, Enjoy Music Wirelessly From Up To 150 Feet Away Through 900MHz Technology and Included Transmitter