Fermi estimate — lightning and thunder

Problem

You see a flash and $7\;\mathrm{s}$ later you hear the thunder. Estimate the distance to the lightning using $v_\mathrm{suono} \approx 343\;\mathrm{m/s}$. What is the equivalent rule of thumb?

Solution

Setup. The light of the flash arrives essentially instantaneously ($c \approx 3\cdot 10^8\;\mathrm{m/s}$, negligible delay); the thunder travels at the speed of sound. The measured delay is therefore the sound’s travel time:

$d = v_\mathrm{suono}\cdot t$

Substitution.

$d = 343\cdot 7 = 2401\;\mathrm{m}$

$\ev{d \approx 2{,}4\;\mathrm{km}}$

Rule of thumb. Since sound travels about $343\;\mathrm{m}$ per second, it takes roughly 3 seconds per kilometre. Just divide by 3 the seconds between flash and thunder to get the distance in km: $7/3 \approx 2{,}3\;\mathrm{km}$, consistent with the calculation.

Linked atoms

Topics: Onde Concepts: Periodo e frequenza Skills: Stime di Fermi