this is a new acoustic classic guitar I have just bought. It has strange sound. when I play the high E string (open) and then immediately touch the string to mute it the guitar keeps playing a similar but different frequency sound for 8-10 seconds. I have found that the lower E and A string resonates (if I touch the lower E and A the sound is gone).
What should I do? Should I take the instrument back to the shop?
This is not a "problem" necessarily. Each string has a natural set of harmonics that are n*(open string frequency). If the note you play matches one of these then that open string will vibrate. The octave and the fifth are the strongest harmonics and the ones most likely to be heard for a long time after excitation. If you play a fretted D on the B string (3rd fret) you should experience vibration of the open D string. This resonance is part of what makes a good full sound on a classical (many texts encourage the student to allow these open resonances to persist while playing). If they become a problem then the guitarist needs to dampen them with their hands as they play (this is part of the technique). What type of guitar is this? Brand, model, etc.
The problem caused by "sympathetic resonance." On any string instrument, the strings actually cause the whole instrument to resonate. So, the vibration of the higher strings is activating those lower strings as well.
Some instruments (like the sitar) are designed specifically to enhance these sympathetic resonances, but if you don't want the lower strings to resonate, you will need to mute them with either your left-hand fingers or right-hand palm.
If the sound is unpleasant, though, you should take it to a guitar tech, so they can take a look at it.
