A big difference is that Aux cable is better in quality (of course also depending on quality and length of cable).
With a wireless Bluetooth signal, the audio is compressed when sent and later decompressed when received. This results in a (slight) loss of data and thus of audio quality. You need good speakers to really hear the difference though.
Here is what happens when you play music over the AUX/headphone/audio jack
Digital File->Decoder->Audio Amplifier->Wire->Speakers.
First the digital file is read, and then the audio is decoded. Then the waveform from that decoded audio is generated, and it is sent over to the audio amplifier. The amplifier turns the tiny voltage into a much higher voltage (compared to itself, not dangerous high voltage) which it sends over the wire. The wire, obviously, transmits the changing voltage to the speakers. The speakers then react by moving, and recreating the sound.
Here is what happens when you play music over Bluetooth:
Digital File->Decoder->Bluetooth Transmitter->Radio Waves->Bluetooth Receiver->Audio Amplifier->Speakers
The digital file is read, then decoded, and then the waveform is generated. Then it is sent over to the bluetooth radio which encodes it again, and then sends that over the air. The receiver gets it, decodes it, and then sends it over to the amplifier. The amp boosts that waveform, then puts it into the speakers.
In theory, the cable should have better sound, as the data is not encoded to be sent over the wireless radio… However, in practice, most people don’t notice any difference. They just enjoy the wireless music. But some people are really sensitive to it, so they can’t stand BT at all.
Bluetooth sends a digital signal using radio waves – a series of 1s and 0s – which your Bluetooth speaker must pick up and then convert into an analog signal. This leads to a small loss of quality – you can only send signals over Bluetooth so quickly, so the data is compressed so less data has to be sent.
Aux cords carry an analog audio signal. Your phone or computer has already converted the audio from 1s and 0s into an actual signal that a speaker needs. This signal alone can operate earbuds and most headphones with no additional hardware, while speakers will amplify it first – the signal is made more powerful, but its shape is not changed.
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