You can graph the voltage. If it's close to sine wave, it's "clean". If it's a mess, it's "dirty". In more precise terms, you can check how much power is in frequencies further away from the main one (50 / 60 Hz depending where you live).
As for the difference in the audio output, it will be very different between different quality audio equipment. On the good side they may go as far as smoothing out the input power internally. On the opposite side, you've got cheap old vinyl players which output a constant 50Hz + harmonics buzz in the output, even with perfectly clean power supply.
http://superuser.com/a/182004/11814
You can graph the voltage. If it's close to sine wave, it's "clean". If it's a mess, it's "dirty". In more precise terms, you can check how much power is in frequencies further away from the main one (50 / 60 Hz depending where you live).
As for the difference in the audio output, it will be very different between different quality audio equipment. On the good side they may go as far as smoothing out the input power internally. On the opposite side, you've got cheap old vinyl players which output a constant 50Hz + harmonics buzz in the output, even with perfectly clean power supply.