Is Building a Radio Transmitter for Wireless Earphones a Feasible Solution?

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Building a radio transmitter for wireless earphones is proposed as a cost-effective alternative to expensive Bluetooth options for MP3 players. The idea involves creating a transmitter that plugs into the MP3 player and transmits music over a short AM frequency to a custom receiver connected to earphones. Concerns are raised about maintaining sound quality with this method. An alternative suggestion includes using FM radio headphones paired with an FM modulator, which could be a more straightforward and affordable solution. Overall, while the DIY transmitter idea is interesting, there are simpler options available that may achieve the desired outcome without compromising sound quality.
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I wanted to get wireless (bluetooth) earphones for my mp3 player but when I checked I found that they were way out of my price range (bluetooth earphones for phones with bluetooth are relatively cheep, but for a regular mp3 player they're expensive ~ 200 dollars).
So I had an idea: I can make a radio transmitter that plugs into where my earphones normally plug in and make it transmit the music at some AM frequency up to about a meter - and then make a tiny radio receiver for that frequency only which I connect to some earphones. The I just have to plug the transmitter into the mp3 and the music will be transmitted to the earphones.
Now, I've never actually built a transmitter before (just the receiver) though I'm pretty sure I know how. So my question is - do you think that this is a feasible solution to the problem? Would it be possible to build a transmitter that didn't substantially lower the sound quality? Are there better solutions to this problem?
Thanks.
 
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How about some fm radio headphones and a fm modulator like they sell for playing mp3's in your car. It would all be < $50 I would think.
 
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