Since the audio output jack on my iMac has died and repair, according to MAC, is very expensive. I have navigated all over the web and have concluded a) that purely wifi headphones don't exist, only bluetooth.
Are there any headphones, wifi or bluetooth whatever as sensitive as my Bose speaker, that is, that can receive music and voice from my iMac a floor above or a floor below the modem and iMac. Some catalogues suggest 10 straight-line meters wifi from source to headphones is all anyone can hope for, and I've had bad luck trying to use a bluetooth audio adapter hooked up to a traditional audio device (speaker or headphones with wire).
Sorry about your iMac's audio output issue - but out of curiosity, what price was quoted to fix the jack? Also, have you tried a can of compressed air in the jack opening (gently of course)?
Since Wi-Fi is a networking standard (802.11...) working on the 2.4 GHz and/or 5 GHz RF spectrum band, I don't believe that a set of wireless headphones can use its specifications.
The Bluetooth (BT) to audio jack adapter would seen like a simple solution, but as stated you have not had good experience w/ that option - Amazon
HERE has a lot of offerings but the ratings are so variable - I guess that 'trial & error' might be needed to find one that works well for you?
For myself, I have 2 wireless headphones: 1) Rocketfish BT - work well but the wireless range is about 30 ft as you have noted; again you likely would have to buy a set and test in your area; and 2) Sennheiser RS160 which I have plugged into my audio receiver's headphone jack - uses the 2.4 GHz band and work well; but of course you would need the BT-audio jack adapter for your iMac.
Hopefully, others will 'chime in' w/ different solutions - Dave

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