b
(b) If suppose \(n_S\) = frequency of string \( = \frac{1}{{2l}}\sqrt {\frac{T}{m}} \)

\(n_f\) = Frequency of tuning fork \(= 480 Hz\)

\(x =\) Beats heard per second \(= 10\)

as tension \(T\) increases, so \( n_S\) increases (\(\uparrow\))

Also it is given that number of beats per sec decreases (i.e. \(x\downarrow\))

Hence \( n_S\uparrow -n_f = x\downarrow\) ... \((i)\) \(\rightarrow\) Wrong 

\(n_f -nS\uparrow = x\downarrow\) ... \((ii)\) \(\rightarrow\)  Correct

\(\Rightarrow\) \(n_S = n_f -x = 480 -10 = 470 Hz.\)