Can anyone show me how to work this problem out?

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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."
 

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  • #2
Doc Al
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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?
 
  • #3
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I think doc al gave it away. :approve:
 
  • #4
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[tex]\Delta t=t_{stop}-t_{start}[/tex]
[tex]\Delta t=s[\frac{1}{v_{sound}}-\frac{1}{v_{light}}][/tex]
For s = 1 km,
[tex]\Delta t=2.9s=3s[/tex]
n=3 s
 

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  • #5
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...
 
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  • #6
Doc Al
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needhelpperson said:
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. :wink:
 

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