Calculating distance can be a fun and practical application of physics. When you see lightning but hear thunder a few seconds later, you are experiencing this concept firsthand! To calculate how far the lightning struck from you, you must know the time it took for the sound to travel and the speed of sound in that medium, which is the air for this scenario.
The famous formula to determine distance is:
Using this formula means you determine how many meters the sound travels each second after the lightning flash. You multiply this rate (or speed) by the number of seconds it takes for you to hear the thunder.
In our original exercise, the time is 3.5 seconds, and we know the speed of sound is 340 m/s. Plug these values into the formula:
\[\text{Distance} = 340 \, \text{m/s} \times 3.5 \, \text{s}\]Doing the calculation yields:
\[\text{Distance} = 1190 \, \text{meters}\]The sound of thunder took 3.5 seconds to travel 1190 meters, showing how this back-of-the-envelope calculation accurately represents your proximity to the original lightning flash.