Question

The frequency (n), of a tuning fork, depends upon the length (l) of its proungs and the density (d) and Young’s modules (Y) of its material, through the relation

n = \(\frac{k}{l}\sqrt{\frac{Y}{d}}\)

If the relative percentage errors, in the determination of n, l and d are 0.1%, 0.5% and 1%, respectively, the relative percentage error, in the determination of Y, would be

(1) 2.2%

(2) 1.6%

(3) 1.1%

(4) 0.95%

Answer 1

(1) 2.2%

We have,

\(n =\frac{k}{l}\sqrt{\frac{Y}{d}}\)

∴ Y = \(\frac{n^2l^2d}{K^2}\)

∴ \(\frac{ΔY}{Y}=2\frac{Δn}{n}+2\frac{Δl}{l}+\frac{Δd}{d}\)

= 2 (0.1%) + 2(0.5%) + (1%) 

= 2.2 %