Hey Richard -- if it's easy for you to shoot a little video of this happening, that might help.

Is this resonating coming out of an amp, or is it coming from the body of your guitar (unplugged)? If it's coming out of the guitar itself (not plugged in), it might be a part on it loose or vibrating. If you're on an electric, it's possible that it's a string resonating back behind the bridge, or the springs in your tremolo (in which case you can stick little rubber bands in them -- I do this on some of my guitars to stop that sound).

Brand and model of guitar and any other details can help...

-Carl.