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Distance Costs Decibels

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Distance Costs Decibels

The general formula for the number of decibels corresponding to a change in sound intensity to relative to the former intensity is

Part A
Suppose that a sound has initial intensity measured in decibels. This sound now increases in intensity by a factor . What is the new level of sound ?
Express your answer in terms of and the factor , using for the log base 10.

Part B
Find the change in intensity of a point source of sound that results from moving the listener initially at a distance to a distance from the source .
Express the change in intensity in terms of and , using for the logarithm of base 10.

Part C
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Solution Preview

As I have difficulty editing equations in your Word file, I am writing the answers here, and using "b" instead of "beta", "log10" to say "log with base 10", etc

The definition of the difference in decibels between two intensities f1 and f2 is

b2 = ...