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I would like to understand the implications of wired versus wireless sound signal transmission. Say, the signal originates from a source and arrives to an amplifier via cable. Is there a difference if the amplifier is connected to the speaker via cable or over Bluetooth in terms of master volume level?

Is that correct that because only digital signal can be transmitted wirelessly, anything the amplifier adds is lost in that case and only a wired connection can transmit the amplified signal?

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The role of an audio power amplifier (be it a traditional hifi amplifier, the embedded amplifier in powered loudspeakers, or the small amplifier that drives the headphones of your smartphone) is to provide the electrical power to physically move the speakers (not all of them are properly loudspeakers, but for simplicity I'll just say speakers). Radio waves are not very efficient to transmit a large amount of power, and that's why you have to use cables to connect a power amplifier to its speakers.

If you wish to actuate the speakers wirelessly, you need to put an amplifier closer to them and transmit a low energy signal to that amplifier. This transmission doesn't have to be digital, in fact that's what AM or FM radio has been doing for decades.

But it can be digital, and that's indeed the case with bluetooth. The useful information carried for music playback by a bluetooth connection is pretty similar (conceptually) to the content of an MP3 or WAV file you may find in your computer or smartphone. So it's up to the bluetooth receiver device to decode and amplity that signal in order to playback the music.

In summary, whatever the setup, the loudspeaker and the power amplifier that is driving it are allways within a relatively short distance and cable connected.

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The answer by joseem is partially correct. What is missing is the issue of dynamic range and the source or transmission format. MP3's have dynamic range (loudest to softest sound with no noise, hissing or distortion) of about 60dB (14 bits), the same as the best vinyl records or cassette tapes.

CD audio is a .wav file and has about 90dB (16 bits) of dynamic range, a huge improvement over MP3 but not the best.

The gold standard is SACD used in movies, movie theaters, and live concert recordings. Dynamic range is 120dB (24 bits), with no background noise or hiss even at full volume. It can simulate a gun-shot sound close to real-world sound levels.

This is the one setup where only wired connections and high-performance equipment can reproduce the scary realism of SACD sound. This would be one setup that would overload and distort a Bluetooth or most any RF signal. The amplifier and speakers must be of very good quality.

I just wanted to point this issue out in case you do use SACD or a DVD or Blu-Ray disc as a source and wonder why the Bluetooth is distorted, but wired connections sound clean, with awesome dynamic range.

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user18060 is wrong about mp3s not having the dynamic range of wav or sacd. The dynamic range of mp3 is theoretically 486dB according to Csaba Horvath in this article http://www.tonestack.net/articles/digital-audio-compression/mp3-aac-dynamic-range.html I agree that RF analog signals are not licensed to have the dynamic range of a cd.

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