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On a cloudy day, the sound of thunder was heard 4.5 s after the flash of light was seen. How far was the cloud? Given that speed of sound = 340 m/s

This is what I've tried:

speed of light(c) = 10^6 * speed of sound(v)

therefore, speed of light=340*10^6 m/s

If x is the distance of the cloud, then

x/(340*10^6)  -  x/340 = 4.5

=>(340*10^6  -  340)/x =  1/4.5
=> x=1529998470`

but the correct answer is 1530m . Where am I going wrong?

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closed as too localized by Qmechanic Feb 15 '13 at 15:24

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1 Answer 1

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The simple answer is that the question assumes you see the lighting immediately i.e. you assume the speed of light is infinite and you don't need to take account of it. If you want to take the speed of light into account this is how you'd do it:

If the cloud is $x$ metres away then the times taken by the light flash and sound are:

$$t_{light} = \frac{x}{c} $$

$$t_{sound} = \frac{x}{v} $$

where $c$ is the speed of light and $v$ is the speed of sound. All you know is that there is a 4.5 second difference between the times:

$$ t_{sound} - t_{light} = 4.5 $$

If we substitute for $t_{sound}$ and $t_{light}$ using the first two equations we get:

$$ \frac{x}{v} - \frac{x}{c} = 4.5 $$

and rearranging this gives:

$$ x = \frac{4.5}{1/v - 1/c} $$

Putting $v$ = 340m/s and $c$ = 3 $\times$ 10$^8$ gives $x$ = 1530.002 and this is only a tiny bit bigger than the result if you ignore the finite speed of the light.

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