Aviolinist tuning her violin plays her a-string while sounding a tuning fork at a 415 hz, and hears 5 beats per second. when she tightens the string, the beat frequency decreases. what should she do to tune the string to a, and what was the original untuned freq of her string

410 Hz

Explanation:

It is given that frequency of tuning fork is 415 Hz and hears a beat of 5 beat per second

so untuned frequency must be either 410 Hz or 420 Hz because beat frequency is the difference in frequency of two notes.  

When she tightens the string the beat frequency decrease

and velocity

where

where T=tension

it T increase v also increases and from 1 st equation frequency is also increasing therefore untuned frequency must be 410 Hz because beat frequency is decreasing.                    

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explanation:

real, smaller and upside-down.   so the answer should be b.