Question

w One of the loudest sounds in recent history was that made by the explosion of Krakatoa on August 26-27, 1883.According to barometric measurements, the sound had a decibel level of 180 dB at a distance of 161 km. Assuming theintensity falls offas the inverse of the distance squared, what was the decibel level on Rodriguez Island, 4 800 km away?

Answer 1

The decibel level is 0.203 dB.

Step-by-step explanation:

The relationship between the sound intensity, I, and the distance, r, is given below:

`I\alpha (1)/(r^(2))`

Therefore,

`I=(k)/(r^(2))`

∴
`Ir^(2) =Constant ...... (1)`

So
`I_(1) r_(1)^(2) = I_(2) r_(2)^(2)`

`I_(2) =I_(1)((r_(1))/(r_(2)))^(2)` ....... (1)

Fitting the given terms into equation (1), we can obtain the decibel level on Rodriguez Island:

`I_(2) =180((161 km)/(4800km))^(2) \\\\I_(2) = 0.203 dB`