To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density ρ of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to S1/n. The value of n is

Engineering

Physics

Dimensions

Question

To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density ρ of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to S^1/n. The value of n is

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d = k r^x s^y f^z

L = [ML^–3]^x [MT^–3]y [T^–1]^z

x + y = 0

–3y – z = 0

1 = –3x $\Rightarrow x = \frac{- 1}{3}, y = \frac{1}{3}$

⇒ x = 3