Question

In a resonant column method, resonance occurs at two successive levels of $l_1=30.7cm$ and $l_2=63.2cm$ using a tuning fork of $f=512Hz$. What is the maximum error in measuring speed of sound using the relations $v=f\lambda$ and $\lambda =2(l_2-l_1)$?

• A. $256cm/sec$
• B. $92cm/sec$
• C. $128cm/sec$
• D. $102.4cm/sec$

Answer 1

Answer: (D)

$102.4cm/sec$

The maximum error is given by :

$c=f\lambda =512\times 2(l_2-l_1)=512\times 2\times (63.2-30.7)=332.8m/s$

$\frac{\Delta c}{c}=\frac{\Delta f}{f}+\frac{\Delta \lambda }{\lambda }$

Least count of scale $=0.1cm$

total error in measurement of $\lambda$

$\Rightarrow 2\times L.C.=0.2cm$

Total error in measurement of $f$ $\Rightarrow 0$

$\frac{\Delta c}{332.8}=\frac{0}{f}+\frac{0.2}{65}$

$\Delta c=\frac{0.2}{65}\times 332.8=1.024m/s=102.4cm/s$