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Two identical sonometer wires have a fundamental frequency of $500 \mathrm{~Hz}$, when kept under the same tension. What fractional increase in the tension of one wire would cause an occurrence of 5 beats $/ \mathrm{sec}$, when both wires vibrate together? A 2 B 3 C 4 D 5
Two identical sonometer wires have a fundamental frequency of $500 \mathrm{~Hz}$, when kept under the same tension. What fractional increase in the tension of one wire would cause an occurrence of 5 beats $/ \mathrm{sec}$, when both wires vibrate together?
A 2
B 3
C 4
D 5
Physics | Previous Year Question Papers
Two identical sonometer wires have a fundamental frequency of $500 \mathrm{~Hz}$, when kept under the same tension. What fractional increase in the tension of one wire would cause an occurrence of 5 beats $/ \mathrm{sec}$, when both wires vibrate together?
A 2
B 3
C 4
D 5

Solution (A) 2
$\mathrm{n} \propto \mathrm{V}$
and $\mathrm{V} \propto \sqrt{T}$
$$
\Rightarrow \mathrm{n} \propto \sqrt{\mathrm{T}} . .(1)
$$
5 beats/sec are obtained when the frequency of one become $505 \mathrm{~Hz}$ i.e. percentage increase in frequency is $1 \%$
From (1) Percentage increase in $\eta=1 \%$
$\Rightarrow \%$ increases in tension $=2 \%$
(Note that method is applicable for small changes only)

i

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