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  4. A tuning fork of frequency 200 Hz is in unison with a sonometer wire. The number of beats heard per second when the tension is increased by 1 % is

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Q. A tuning fork of frequency $200\, Hz$ is in unison with a sonometer wire. The number of beats heard per second when the tension is increased by $1 \%$ is

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Solution:

$\frac{n_{2}}{n_{1}}=\sqrt{\frac{101}{100}}=\left(1+\frac{1}{100}\right)^{1 / 2}=1+\frac{1}{200}$
(From Binomial Expansion)
$n_{2}=n_{1}+\frac{n_{1}}{200}$
Number of beats $s ^{-1}=n_{2}-n_{1}=\frac{n_{1}}{200}=\frac{200}{200}=1$