What do you mean, cannot change its magnitude easily? I can just pluck it harder or softer? Do you mean frequency response?
And the bandwidth of a resonant circuit depends on its Q. Hence my question about a wet string’s Q, which might well be different from a guitar string’s Q.
Was the bandwidth that narrow at the resonant frequency? Intuitively, I wouldn't have expected that "wet string" has a high Q. :)
If I had been your student, I would have had great fun with it.