What is the value of n for 1 km distance between seeing and hearing an event?

[needhelpperson]

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."

$$\Delta t=t_{stop}-t_{start}$$
$$\Delta t=s[\frac{1}{v_{sound}}-\frac{1}{v_{light}}]$$
For s = 1 km,
$$\Delta t=2.9s=3s$$
n=3 s

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 traveled 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...

 

[Alkatran]

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.

 

[Leong]

needhelpperson,
Sound traveled 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.

 

[needhelpperson]

needhelpperson,
Sound traveled 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.

 

[Leong]

Sound traveled a distance during that time 340 * a =
$$340*\frac{10^3}{3*10^8}=\frac{34*10^4}{3*10^8}\\ =\frac{34}{3*10^4}\\=\frac{17}{15000}$$

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