A tuning fork of known frequency $256\,Hz$ makes $5$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
AIEEE 2003, Medium
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(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.$
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