If a tuning fork of frequency (.f0.) 340 Hz and tolerance ±1 % 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 = text74.70 cm , then the permissible error in speed of sound is

Question

If a tuning fork of frequency (.f0.) 340 Hz and tolerance ±1 % 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 = text74.70 cm , then the permissible error in speed of sound is (A) 1.2 % (B) 1.8 % (C) 1 % (D) 0.8 %

Tardigrade Admin · Accepted Answer

V =2 f 0( l 2-11) let l 2-11=x l 1=(24.0 ± 0.1) cm l 2=(74.70 ± 0.01) cm l 2-11=(50.70 ± 0.11) cm beginaligned (Δ x/x) &=((0.11/50.70)) Δ x % &=(0.11/50.70) × 100 &=0.22 % Δ V % &=Δ f 0 %+Δ x % &=1.22 % &=1.2 % endaligned

Q. If a tuning fork of frequency $(f_{0})$ $340 Hz$ and tolerance $\pm 1%$ is used in the resonance column method for determining the speed of sound. If the first and the second resonance are measured at $l_{1} = 24.0 c m$ and $l_{2} = 74.70 c m$ , then the permissible error in speed of sound is

$1.2%$

$1.8%$

$1%$

$0.8%$

$V = 2 f_{0} (l_{2} - 1_{1})$
let $l_{2} - 1_{1} = x$
$l_{1} = (24.0 \pm 0.1) c m$
$l_{2} = (74.70 \pm 0.01) c m$
$l_{2} - 1_{1} = (50.70 \pm 0.11) c m$
$\frac{Δ x}{x} Δ x % Δ V % = (\frac{0.11}{50.70}) = \frac{0.11}{50.70} \times 100 = 0.22% = Δ f_{0} % + Δ x % = 1.22% = 1.2% < b r / >$

Q. If a tuning fork of frequency (f0​) 340Hz and tolerance ±1% is used in the resonance column method for determining the speed of sound. If the first and the second resonance are measured at l1​=24.0cm and l2​=74.70cm , then the permissible error in speed of sound is

1.2%

1.8%

1%

0.8%