How accurate is the thunder/lightning rule?

Question

In a thunder and lightning storm there is a rule of thumb that many people follow. After seeing the lightning, count seconds to yourself. If it takes 5 seconds for the sound of thunder to reach you, then the lightning bolt was one mile away from you. Sound travels at a speed of 331 meters/second. How accurate is the rule of thumb? Express your answer as a precent error.

I this is for my stupid problem solving class that I HATE. If you solve it, you will be my hero and I will love you forever.

Answer 1

Rule says: distance = elapsed time/ 5 seconds * 1 mile
= elapsed time/ 5 seconds * 1609.344m
= elapsed time / 321.8688m

Exact answer: distance = elapsed time/ 331 m/s

Relative error: (1/331 - 1/321.8688)/ (1/321.8688)
= -0.028
in pct:
100% * (1/331 - 1/321.8688)/ (1/321.8688) = -2.8%

So the distance estimate is an underestimate by 2.8%

Answer 2

Distance = speed x time

if speed of sound is 331 meters per second,
and it took 5 seconds for the sound of thunder to reach you,

Distance = (331 meters/sec) * 5 seconds
Distance = 1655 meters

We cant compare 1655 meters versus 1 mile yet because they have different units.

The conversion factor is :
there are 1600 meters for every mile

Therefore we can now compare to get the percent error:

correct distance = 1655 meters
estimated distance = 1 mile = 1600 meters

percent error = [ (estimated distance - correct distance) / correct distance ] x 100%

percent error = [ (1600 - 1655) / 1655 ] x 100 %
percent error = ( -55 /1655 ) x 100 %
percent error = -3.32 %

The answer is negative because we underestimated the actual distance. Had our estimate been bigger than the actual, the percent error would have been positive.

Answer 3

First -- light travels so fast that you see the lightening almost at the same instance of when it hits.

Second -- if sound travels at 331 m/s, then in five seconds it will have travelled 1655 meters.

Third -- there are 1609.334 meters per mile.

Fourth -- the error is 35.666 meters. Divide this by 1609.334 to get the percent error of 2.834%

Answer 4

Ok so we know that sound travels approx. 330 meters per second or 1140 feet per second right. If there are 5280 feet in a mile, simple math tells us that sound will travel a mile in around 4.63 seconds if you take 5280 and divide 1140 into it. So can we say thunder travels a mile in about five seconds? Sure why not but your percent error is around 7% because we know that 7 percent of 5 is .35 and the difference is .37 off the top of my head. Is that accurate enough?

Answer 5

Pretty close. I mile is about 1620 meters, and this rule indicates a distance of 1655. So you are talking about 40 meters in 1600 or about 2.5 pct.

Answer 6

Lightning Distance Rule

Answer 7

In science class, the teacher told us that the sound travels around 1 km per hour.