Two identical wires are vibrating in unison. If the tension in one of the wires is increased by $2 \%$, five…

Two identical wires are vibrating in unison. If the tension in one of the wires is increased by $2 \%$, five beats are produced per second by the two vibrating wires. The initial frequency of each wire is $(\sqrt{1 \cdot 02} \doteq 1 \cdot 01)$
  1. $1000 \mathrm{~Hz}$
  2. $500 \mathrm{~Hz}$
  3. $400 \mathrm{~Hz}$
  4. $200 \mathrm{~Hz}$

Solution

$\mathrm{n} \propto \frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \quad \therefore \mathrm{n} \propto \mathrm{T}$ $\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}=\sqrt{\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}}=\sqrt{\frac{1.02 \mathrm{~T}_{1}}{\mathrm{~T}_{1}}}=\sqrt{1.02}=1.01$ Also $\mathrm{n}_{2}-\mathrm{n}_{1}=5$ $\therefore 1.01 \mathrm{n}_{1}-\mathrm{n}_{1}=5 \quad \therefore 0.01 \mathrm{n}_{1}=5$ $\therefore \mathrm{n}_{1}=\frac{5}{0.01}=500 \mathrm{~Hz}$ :

Asked in: MHT CET 2020 (12 Oct Shift 1)

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