A string musical instrument was first plucked with a force of smaller magnitude and then with a force of greater magnitude. In which case would the instrument produce a louder sound?

Dear student,

The loudness of sound depends upon the amplitude of vibration. The amplitude of string is larger when it is plucked with greater force and hence the sound will be louder in that case. 

Regards

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loudness of the sound produced by a vibrating object depends on the amplitude of vibration. Loudness is proportional to the square of the amplitude. Thus, if the amplitude is increased by three times, the loudness increases by nine times.
I think the second is the answer when there was a greater force of magnitude
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