How to measure using an external source?

In some cases it is more convenient to use an external source than to use the sound card output for playing the measurement signal. For example if the source is placed very far away from the microphone (a wireless transmission is also an alternative in this case). Another example is a sound system that does not have any direct input except a CD-player.

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Measure with signal from a CD-player

Measure with DAT/MD/CDR as external source

Detection of arrival time does not seem to be right, why?