How Do You Calculate Decibel Intensity at a Distance in Spherical Waves?

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To calculate decibel intensity at a distance of 100m from a spherical wave source with an initial intensity of 8.0 W/m^2 at 1.0 m, the intensity decreases with the square of the distance due to the inverse square law. The original decibel level is calculated using the formula β=10log(I/I0), where I0 is the reference intensity of 10^-12 W/m^2. The confusion arises from the dual use of "decibel" for both relative and absolute intensities, necessitating clarification of reference levels. The intensity at 100m can be found by applying the inverse square law to determine the new intensity before converting it to decibels. Understanding these principles is crucial for accurate calculations in acoustics.
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Homework Statement


The intensity of a certain spherical wave is 8.0 W/m^2 at a distance of 1.0 m from the source. If the medium is isotropic and nonabsorbing, calculate the decibel intensity 100m from the source.

Homework Equations


β=10ln(I1/I0)

The Attempt at a Solution


I know how to use these equations... And to find the original dB level i use
β=(10dB)ln(8.0/10^-12)

Im just not sure what to do to find intensity 100m away?
 
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What do you mean with "original dB level"?

How does intensity depend on distance for spherical waves without absorption?
 
"Decibel" is very confusing because the term is used both for relative and absolute intensities. As far as I am aware, the unit dB always denotes (or should always denote) a relative intensity. If an absolute intensity is intended then it should be qualified to indicate the reference level, like dBm or dBmW.
Where does your 10-12 come from?
 
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