Have you ever met someone and had an immediate sense of peace that lasted for weeks?

No. But the first time I heard a recording of my husband's voice (before I ever met him) was the first full night of sleep I had had in months. I had been suffering from pneumonia for about seven months at the time and was waking during the night with coughing fits. And when I did finally sleep there were nightmares. Listen to him sing and no more nightmares, no coughing. Just peaceful deep dreamless sleep.