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STD 11 - 14. waves and sound — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 14. waves and sound4 Marks
Question
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
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Answer

(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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