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Question
The sound produced by a thunderstorm is heard 10 s after the lightning is seen. Calculate the approximate distance of the thunder cloud. (Given the speed of sound = 340 m s–1.)
Solution
Let the distance of thunder cloud from observer be x m.
Now, speed of light = 3 x 108 ms−1
Speed of sound = 340 ms−1
Time is taken by the light to reach the observer,
`"t"_"l" = "x"/(3 xx 10^8) "S"`
Time is taken by the sound to reach the ``observer,
`"t"_"l" = "x"/340 "S"`
Given, t8 − t1 = 10s
`"x"/340 - "x"/(3 xx 10^8) = 10` or `"x"(1/340 - 1/(3 xx 10^8)) = 10`
`"x"/340 = 10` (∵ 3 × 108 >>> 340, ∴ `1/340` >>> `1/(3 xx 10^8)`)
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