Calculating Sound Intensity and Pressure Variation at a Distance

[Ian Baughman]

Homework Statement

A speaker blares out music with a power of 10 W. Assuming the air has a temperature of 50°F and a pressure of 1 atm, what is the sound intensity level in decibels at a distance of 100m away? What is the maximum pressure variation at that point? What is the distance at which the intensity is 50 dB? The air has an effective molar mass M = 28.8 g and a ratio of heat capacities γ = 1.40.

Homework Equations

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1) I = P/(4πr²)
2) β = (10 dB)log(I/I₀)

The Attempt at a Solution

1) I used equation #1 where P = 10 W and r = 100 m to find:

I = 7.96 ×10^-5 W/m²​

2) This is where I'm having difficulty. I'm not quite sure on how to find I₀. I know I can't use the above equation but I can't seem to find any other information that would be helpful.

 

[TSny]

I₀ is a standard value of intensity that should be given in your textbook or notes.

 

[Ian Baughman]

So I found a value, I₀ = 10^-12 W/m². Where does this value come from though?

 

[TSny]

So I found a value, I₀ = 10^-12 W/m². Where does this value come from though?

It corresponds to the human "threshold of hearing" at 1000 Hz . See http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/intens.html#c3

 

[Ian Baughman]

Thank you!