A string is fixed at both ends. The tension and density of the string are accurately known but the length and the radius of cross section are known with some error. If maximum errors made in the measu

Question

A string is fixed at both ends. The tension and density of the string are accurately known but the length and the radius of cross section are known with some error. If maximum errors made in the measurement of length and radius are 1% and 0.5% respectively then the maximum possible percentage error in the calculation of the fundamental frequency of the string is:

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Answer:

C

Solution:

$f = \frac{1}{2 L} T / μ$ and $μ = ρ π r^{2}$ , so $f \propto 1/ (L r)$ . $Δ f / f = Δ L / L + Δ r / r = 1% + 0.5% = 1.5%$ .

TestHub · Accepted Answer

f = 2 L 1 ​ T / μ ​ and μ = ρ π r 2 , so f ∝ 1/ ( L r ) . Δ f / f = Δ L / L + Δ r / r = 1% + 0.5% = 1.5% .

Physics - Wave on String Question with Solution | TestHub

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