Problem — Why thunder arrives after lightning

Problem

Why thunder arrives after lightning. A storm is $3\;\text{km}$ away. (a) Why do you see the lightning “instantaneously” but hear the thunder about $9\;\text{s}$ later? (b) A friend claims that “lightning and thunder are two different phenomena occurring at different times”. Is this correct? (c) How would the delay change if the air were colder? Answer by relating the speeds of electromagnetic waves and sound.

Solution

(a) Light (an electromagnetic wave) travels at $c \approx 3\cdot 10^{8}\;\text{m/s}$: for $3$ km it takes $\sim 10^{-5}\;\text{s}$, effectively instantaneous. Sound travels at $v \approx 340\;\text{m/s}$: for $3$ km it takes

$t = \frac{d}{v} = \frac{3000}{340} \approx 9\;\mathrm{s}$

Hence the rule of thumb: $\sim 3$ seconds of delay for every km.

(b) No, this is not correct. Lightning and thunder are the same event (the lightning discharge), which simultaneously emits light and sound. The difference in arrival time is due solely to the different propagation speeds of the two waves, not to two separate events.

(c) The speed of sound in air decreases as the temperature drops ($v \propto \sqrt{T_\text{absolute}}$). With colder air, sound is slower, so the delay between lightning and thunder increases (for the same distance).

Collegamenti

Argomenti: Waves Concetti: Period and Frequency