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If a tuning fork of frequency $\left ( f_{0} \right )$ 340Hz tolerance $\pm 1^{o}/_{o}$ is used in resonance column method $\left [ v=2f_{0}\left ( l_{2}-l_{1} \right ) \right ],$ the first and the second resonance are measured at $l_{1}=24.0\; cm\; and\; l_{2}=74.0\; cm.$ The max. permissible error in speed of sound is :
Option: 1
$1.4\; ^{o}/_{o}$

Option: 2
$1.8\; ^{o}/_{o}$

Option: 3
$1\; ^{o}/_{o}$

Option: 4
$0.8\; ^{o}/_{o}$

Answers (1)

best_answer

Error in division x = a/b -

$\frac{\Delta x}{x}=\pm \left ( \frac{\Delta a}{a}+\frac{\Delta b}{b} \right )$

( maximum fractional error in $x$ )

- wherein

$\Delta a$ = absolute error in measurement of a

$\Delta b$ = absolute error in measurement of b

$\Delta x$ = absolute error in measurement of x

$\left [ \frac{\Delta v}{v} \right ]_{max}=\frac{\Delta f_{0}}{f_{0}}+\frac{\Delta l_{1}+\Delta l_{2}}{l_{2}-l_{1}}=\frac{1}{100}+\frac{0.1+0.1}{74\;- \; 24}$

$=\left [ \frac{1}{100}+\frac{0.2}{50} \right ]\times 100^{o}/_{o}=1.4^{o}/_{o}$

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