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 the intensity falls off as the inverse of the distance squared, what was the decibel level on Rodriguez Island, 4,800 km away?

Answer: 150.51 dBStep-by-step explanation:Data provided in the question: decibel level of sound at 161 km distance = 180 dBd₁ = 161 kmd₂ = 4800 kmI₁ = 180 dbThe formula for intensity of sound is given as:I = [tex]10\log(\frac{I_2}{I_1})[/tex]and the relation between intensity and distance is given as:I ∝ [tex]\frac{1}{d^2}[/tex]orId² = constantthus,I₁d₁² = I₂d₂²or[tex]\frac{I_2}{I_1}=\frac{d_1}{d_2}[/tex]therefore,I = [tex]10\log(\frac{d_1}{d_2})^2[/tex]orI = [tex]10\times2\times\log(\frac{161}{4,800})[/tex]orI = 20 × (-1.474)orI = -29.49Therefore,the decibel level on Rodriguez Island, 4,800 km away= 180 - 29.49= 150.51 dB