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When the tension in a string is increased by 44%. the frequency increased by 10Hz. The frequency of the string is

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a

200 Hz

b

100 Hz

c

150 Hz

d

50 Hz

answer is D.

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Detailed Solution

$\begin{aligned} f = \frac{n \sqrt{\frac{T}{μ}}}{2 l} = \frac{n \sqrt{T}}{2 L \sqrt{μ}} \\ \Rightarrow \frac{f_{1}}{f_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \end{aligned}$

$\begin{aligned} \to \frac{f}{f + 10} = \sqrt{\frac{100}{144}} = \sqrt{144} f = \sqrt{100} f + 100 \\ \begin{aligned} 12 f & = 10 f + 100 \\ 2 f & = 100 = f = 50 Hz . \end{aligned} \end{aligned}$

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