My wife did this with a cable. Treadmill makes so much noise, she can't hear the TV. Now she wants me to amplify with speakers.
I had a similar issue with the tv in our bedroom. I like to watch tv at night while laying in bed, but my wife would always tell me to turn the tv down because it was disturbing her. So the lower I made it meant I could not hear it.
I tried the TX/RX Bluetooth devices out there, but they all had so much lag between the sound and the picture that it made watching tv really weird. It was especially bad when someone on the screen would talk. I would see their mouths move, and then about a second later I would hear it. It was like watching one of those old Godzilla movies.
I bought a wireless headset and transmitter from Amazon and it works great. You attach the transmitter up to either the outputs of the tv or the outputs of a set top box, and then plug the transmitter cord into an electrical outlet to give it power.
You charge the headset up by plugging them into the 1/8 inch male jack that is on the transmitter. The charge lasts for a pretty long time, and the range of the headset is about 40 feet from the transmitter.
The headset has it's own volume control, so the tv volume can be turned all the way down if you want, so that no one can hear it except the person wearing the headset.
The downside is that since these are NOT Bluetooth, you have to have line-of-sight between the transmitter and headphones. The farther you get away from line-of-sight, the more interference they get.
This system costs about $40 bucks, so it was cheaper than buying a Bluetooth headset and some kind of Bluetooth transmitter. And this setup works better, at least for my application.
Here is what I have:
Jim