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Two identical string instruments have frequency of $100 \mathrm{~Hz}$ . If tension in one of them increases by $4 \%$ and they are sounded together, then the number of beats - in $1\: \mathrm{sec}$ are -

Option: 1
$1$

Option: 2
$8$

Option: 3
$4$

Option: 4
$2$

Answers (1)

best_answer

Use, $\mathrm{f \propto \sqrt{\bar{T}}\: or \: f \alpha T^{1 / 2}}$
$\%$ increase in $f=\frac{1}{2}$ (% increases in $\mathrm{T}$ )

$\mathrm{ f=\frac{1}{2} \times 4=2 \% }$

$\mathrm{ f_1=100 \mathrm{~Hz}}$

and $\mathrm{f_2=100+2 \% \: of \: 100=102 \mathrm{~Hz}}$

Beat frequency, $\mathrm{f=f_2-f_1}$

$\mathrm{f=2 \mathrm{Hz}.}$

Hence option 4 is correct.

Posted by

Deependra Verma

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