Finding n for distance from light and sound speeds

[phywhat]

Can anyone show me how to work this problem out?

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."

 

[Doc Al]

Welcome to PF!

Here's a hint: for all practical purposes you can treat the light as arriving instantly compared to the sound. So... how long does it take the sound to travel 1 km?

 

[Nenad]

I think doc al gave it away.

 

[Leong]

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

 

[needhelpperson]

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...

 

[Doc Al]

but 3 is not the exact answer is it?

But neither is 3 x 10^8 m/s the exact speed of light, nor 340 m/s the exact speed of sound.

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

I think you've missed the point of this simple exercise.