The string of a violin emits a note of 205 ,H | vedclass

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(C) The initial frequency of the violin string is $f_1 = 205 \,Hz$.When the string is tightened,its tension increases,which leads to an increase in th

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$208$

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(C) The initial frequency of the violin string is $f_1 = 205 \,Hz$.When the string is tightened,its tension increases,which leads to an increase in the frequency of the note emitted.Let the new frequency be $f_2$.The number of beats produced per second is given by the beat frequency $f_b = |f_2 - f_{tuning\,fork}|$.Given that the string produces $6$ beats in $2$ seconds,the beat frequency is $f_b = \frac{6}{2} = 3 \,Hz$.Since the string is tightened,$f_2 > 205 \,Hz$.Therefore,$f_2 - 205 = 3$.Solving for $f_2$,we get $f_2 = 205 + 3 = 208 \,Hz$.

The string of a violin emits a note of $205 \,Hz$ at its correct tension. The string is tightened slightly and then it produces six beats in two seconds with a tuning fork of frequency $205 \,Hz$. The frequency of the note emitted by the taut string is .......... $Hz$.

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