On August 26-27, 1883 in Indonesia on the island of Krakatau,a cataclysmic volca

Question

On August 26-27, 1883 in Indonesia on the island of Krakatau,a cataclysmic volcano eruption occurred, producing the loudestsound recorded in history. It is reported that this explosion was"distinctly heard" as far away as Perth in Australia, approximately3,110km away. 1) Suppose we interpret "distinctly heard" to mean anintensity level of 50 dB, that is, a normal conversation. Usingthis interpretation, find the intensity level 10km fromKrakatau. 2) Do we have enough information to determine the powerproduced by the eruption when the above interpretation is used? Ifyes, calculate the power. If no, explain why it cannot becalculated. 3) How long did it take the sound to travel from Krakatau toPerth? Assume that the average temperature between Krakatau andPerth is 35 °C and that the air is still. On August 26-27, 1883 in Indonesia on the island of Krakatau,a cataclysmic volcano eruption occurred, producing the loudestsound recorded in history. It is reported that this explosion was"distinctly heard" as far away as Perth in Australia, approximately3,110km away. 1) Suppose we interpret "distinctly heard" to mean anintensity level of 50 dB, that is, a normal conversation. Usingthis interpretation, find the intensity level 10km fromKrakatau. 2) Do we have enough information to determine the powerproduced by the eruption when the above interpretation is used? Ifyes, calculate the power. If no, explain why it cannot becalculated. 3) How long did it take the sound to travel from Krakatau toPerth? Assume that the average temperature between Krakatau andPerth is 35 °C and that the air is still.

Explanation / Answer

at r = 3,110km the intensity level = 50 dB, find theintensity level ' at r' = 10 km.
intensity = I
= 10 log(I/Io)
power P = I*4r2, so I = P/(4r2) =constant
= 10 log[P/(4r2Io)] = 10log[P/(4Io)] - 20 log(r)
' = 10 log[P/(4r'2Io)] = 10log[P/(4Io)] - 20 log(r')
' - = 20 [log(r) - log(r')] = 20 log(r/r') = 50 dB
' = 100 dB

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