The speed of light is 3.0*10^8 m/s and the speed of sound is 340 m/s. Find the vaule of the interger n in the following statement:"If you start counting seconds when you see something happen and stop when you hear it happen, for every n seconds counted the event was about 1 km away."

but 3 is not the exact answer is it?

I'll show my calculation.

time take light to travel 1000 m is 1000/(3 *10^8) = a

Sound travelled a distance during that time 340 * a = 1/750 m

So sound should reach there when:

(1000-(1/750)/340 = 749 999/255000 s

so each n = 749 999/255000s for each km

shouldn't the integer be 749999 which happen at 255 km , unless 749999 is not prime...

The value of the inverse of light speed is so much lower than the one of sound that your important digits are never touched by it. (this is a cheat, I know, but it works for checking the answer)

So ... for every second, the sound travels a third of kilometer. The number of second is approximately 3 times the distance in kilometers.

needhelpperson,
Sound travelled a distance during that time 340 * a = 17/(15X10^3) m; then, n = 14999983 / 5100000 second for each km.
n=2.9 s = 3 s.

No, 3 s is not the exact anwer, the exact anwer is as above. but since the question comes with to find the integer n; then i round it to the closest integer.

look at it once more, 340 * a where a is the time for light to travel 1000 m.
And the question was kinda screwed up. "For every n seconds the event was 1 km away". It should've just said, The event happened 1000 km away during the n seconds. Because before, it sounded like we have to find an integer n where for every n seconds the event is 1 km farther.

Sound travelled a distance during that time 340 * a =
[tex]340*\frac{10^3}{3*10^8}=\frac{34*10^4}{3*10^8}\\ =\frac{34}{3*10^4}\\=\frac{17}{15000}[/tex]

Yes, maybe we can say that the question is not clear enough because it makes two person to have two different understandings about it.