Application: Lightning and Thunder or the Relativity of Acoustic Signals

(related to Part: Oddities and Curiosities)

We all know the following effect - first, we see the lightning, then, we hear the thunder. The farther away the storm is, the longer we have to wait between seeing the lightning and hearing the thunder.

In fact, we can use this effect to calculate the distance of the storm from the location we are. The speed of sound equals about $$343 \frac ms$$ (meters per second). This means that if we wait 10 seconds between the lightning and the thunder, the storm's distance to us is

$d(10)=10s\times 343 \frac ms = 3430 \operatorname{meters}\approx 3.4 \operatorname{kilometers}\approx 2.1 \operatorname{miles}.$

Experiments show that the speed of sound neither depends on the height of the tone (the frequency of the sound) nor on its loudness. However, it does depend on the medium in which the sound spreads in. For instance, the speed $$343 \frac ms$$ is only measured if the temperature of the air is $20^\circ$C ($68^\circ$F) and its pressure is 101,3 kPa (kilo Pascal). Changing the temperature or pressure also changes the speed of sound. Also, the speed of sound is totally different in other media then the air (e.g. the speed of sound is about four times as fast in the water - about $$1.484 \frac ms$$.

The relativity of acoustic signals means that if we hear two different events at once, e.g. two shots of two guns, it does not necessarily mean that those two events happened at the same time.

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References

Bibliography

1. WeingĂ¤rtner, Andreas: "Spezielle RelativitĂ¤tstheorie - ganz einfach", Books On Demand, 2016