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

Answer:

The decibel level is 0.203 dB.

Explanation:

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

$I\alpha \frac{1}{r^{2}}$

Therefore,

$I=\frac{k}{r^{2}}$

∴ $Ir^{2} =Constant ...... (1)$

So $I_{1} r_{1}^{2} = I_{2} r_{2}^{2}$

$I_{2} =I_{1}(\frac{r_{1}}{r_{2}})^{2}$ ....... (1)

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

$I_{2} =180(\frac{161 km}{4800km})^{2} \\\\I_{2} = 0.203 dB$