d
(d) Suppose ${n_P} = $ frequency of piano $= ?$ $({n_P} \propto \sqrt T )$
${n_f} = $ Frequency of tuning fork $ = 256Hz$
$x =$ Beat frequency $= 5\, bps,$ which is decreasing $(5→2)$ after clanging the tension of piano wire Also, tension of piano wire is increasing so ${n_P} \uparrow $
Hence $n_P\uparrow-n_f = x\downarrow$ $\rightarrow$Wrong
$n_f -n_P\uparrow= x\downarrow$ $\rightarrow$Correct
$\Rightarrow$$n_P = n_f -x = 256 -5 \,Hz.$