Thanks for your interesting comments. If it happens again I will try just loosening and re-seating the string before I replace it.
New strings can often be the best, quick fix. So happy for you. I had a dulcimer that I had put new strings on that I love on another dulcimer. When I played it, it had lost all life...it sounded muted and lifeless. I love the strings on my other dulcimer. So, I changed strings to a different type and tada, it had it's life back. For whatever reason, that dulcimer just doesn't like those strings. Lesson learned.
Glad that worked out for you. One thing to look at if something like that happens again, it to make sure that the string(s) are firmly and correctly seated in the notches. Sometimes a "violent' strum can dislodge a string minutely, giving rise to those kinds of issues...
I just ran into this problem and I wondered how common this is (I'm a very new dulcimer owner). I began to notice a rather persistent very high harmonic every time I strummed, no matter which strings or notes I was strumming. The more I played, the more I noticed it and the more irritating it became. Today I couldn't stand it any more and began to troubleshoot. It was the A string only, and at first I thought it might be hitting a fret, but even when I was playing on it, it didn't come anywhere near any higher frets. Then I thought it might be resonating with one of the D strings, but careful testing proved that wrong. I thought, OMG, it's a problem with my dulcimer! Argghh! $$$$!! The strange thing was, it was harmonizing with itself--it sounded like a built-in harmonic on the A string all by itself. I thought, what could make that happen? Well, what if there were a defect in the string, a weakness somewhere in it that effectively made it two semi-separate strings, each vibrating at its own rate. With several fingers crossed, I RnR'd the string with a new one. Ta-da—Problem solved! No more irritating sound! And no repair bill! O happy day!