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The frequency of transverse oscillations of a string fixed at both ends is given by $f \propto \frac{\sqrt{T}}{l}$ . Where T is the tension in the string and $l$ is its length. If error in measuring the tension is 2 % and the error in measuring the length is 1 %, the maximum possible error in the frequency is

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2.5 %

3 %

2 %

1.5 %

answer is C.

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Detailed Solution

$f \propto {(T)}^{1 / 2} {(l)}^{- 1}$

$∴ \frac{∆ f}{f} \times 100 % = \frac{1}{2} (\frac{∆ T}{T} \times 100 %) + (\frac{∆ l}{l} \times 100 %)$

$= (\frac{1}{2} \times 2 %) + 1 % = 2 %$

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