   Chapter 14, Problem 13P

Chapter
Section
Textbook Problem

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?

To determine
Decibel level of Rodriguez Island.

Explanation

Given Info: The distance of explosion is 161 km, the distance of a Rodriguez Island is 4800 km, and the explosion of a sound level is 180 dB.

Formula for ratio of sound intensity of a Rodriguez Island is,

I1I2=r22r12

• I1 is the sound intensity at a distance of 161 km
• I2 is the sound intensity at a distance of  4800 m
• r1 is the distance of the explosion
• r2 is the distance of a Rodriguez Island

Formula for difference of decibel levels,

β2β1=10log(I2I1)10log(I1I0)

Simplify the above expression,

β2β1=10log(I2I0I0I1)=10log(I2I1)=log(

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