Question

If a tuning fork of frequency $\left(\right.f_{0}\left.\right)$ $340 \, Hz$ and tolerance $\pm1\%$ is used in the resonance column method for determining the speed of sound. If the first and the second resonance are measured at $l _{1} = 2 4.0 cm$ and $l _{2} = \text{74.70} cm$ , then the permissible error in speed of sound is

• A. $1.2\%$
• B. $1.8\%$
• C. $1\%$
• D. $0.8\%$

Answer 1

Answer: (A)

$V =2 f _{0}\left( l _{2}-1_{1}\right)$
let $\quad l _{2}-1_{1}=x$
$l _{1}=(24.0 \pm 0.1) cm$
$l _{2}=(74.70 \pm 0.01) cm$
$l _{2}-1_{1}=(50.70 \pm 0.11) cm$
$ \begin{aligned} \frac{\Delta x}{x} &=\left(\frac{0.11}{50.70}\right) \\ \Delta x \% &=\frac{0.11}{50.70} \times 100 \\ &=0.22 \% \\ \Delta V \% &=\Delta f _{0} \%+\Delta x \% \\ &=1.22 \% \\ &=1.2 \% \end{aligned}
$