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Would the sound of the headphones be better if I put an additional speaker in each cup?
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I have some closed-back headphones that have poor sound. Is it possible to improve the sound of the headphones by installing additional speakers?
How much better can the sound of the headphones be if the cups are covered with soundproofing tape?
First, you're going to have to define what poor sound means to you. Modding your closed back headphones to add more speakers isn't going to make them sound better, but probably worse.
The best way to get better sound is to replace your headphones with better headphones, or to use a better source when playing music. Even better headphones aren't going to improve the quality of music if you're playing lossy Mp3s.
If your headphones are crappy, a better source won't really help. It's not an or here, headphones make most of the difference. Only decent headphones will appreciably benefit from a good source.
MP3 isn't ideal but, unless you have rather good headphones, 320kbit/s MP3 is pretty damn near transparent.