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 the thunder to reach you, then the lightning bolt is 1 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 percent error.
2007-04-25 08:09:13 · 4 answers · asked by crazy Girly 2 in Science & Mathematics ➔ Mathematics
The original rule-of-thumb was 1,000 ft for every second.
331 m/s = 1085.95801 fps
e = 1 - 1,000/1 085.95801 = 7.9%
Using 5 seconds per mile is a little closer:
e = 2.76%
1,100 fps would be better yet.
2007-04-25 08:40:40 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋
OK, if it takes 5 seconds for the lightning bolt's sound wave to travel one mile, that means that it travels 1,056 feet per second (1 mile = 5,280 feet, so 5,280 divided by 5 = 1,056). So compare that to 331 meters per second. If one meter is 3.281 feet, then you multiply 331 by 3.281 and you get 1,085.95 feet. Next, divide 1,085.95 by 1,056 and you get 1.028. Move the decimal place two places to the right and you get a percent error of 2.8% -- remember, we're talking about a ratio here, so if the ratio was 1:1 the percentage error would be zero because both values would be the same.
2007-04-25 08:22:03 · answer #2 · answered by sarge927 7 · 0⤊ 0⤋
mile = 1760 yards ~ 1609 m
speed of sound = 331 m/s = 331/1609 ~0.206 miles/sec
so 5 sound seconds = 1.028 miles so the rule of thumb is accurate to 3%
2007-04-25 08:47:26 · answer #3 · answered by hustolemyname 6 · 0⤊ 0⤋
1 mile = 1609.34 meters
rule of thumb = 1609.34 m / 5 seconds = 321.87 m/sec
actual sound speed = 331m/sec
% error = {(331 -321.87)/331} * 100 = 2.76%
2007-04-25 08:25:32 · answer #4 · answered by millet_0220 4 · 0⤊ 0⤋