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Two identical strings made of the same material have their fundamental frequencies are 650 \mathrm{kz} and 500 \mathrm{~Hz} respectively. Then the ratio T_{A} / T_{B}

Option: 1

\frac{169}{100}


Option: 2

\frac{100}{169}


Option: 3

\frac{115}{10}


Option: 4

\frac{144}{1000}


Answers (1)

best_answer

$$ \begin{aligned} & f=\frac{1}{2 l} \sqrt{\frac{T}{4}} \\ & f \propto \sqrt{T} \\ & T \propto f^2 \\ & \frac{T_A}{T_B}=\left(\frac{f A}{f B}\right)^{2} =\left(\frac{650}{500}\right)^{2}=\left(\frac{13}{10}\right)^{2} \\ & \frac{T_A}{T_B}=\frac{13}{10} \times \frac{13}{10}=\frac{169}{100} \\ & \frac{T_A}{T_B}=\frac{169}{100} \end{aligned}

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Rishabh

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