Power from Sound: Fans Create 12.56 Watts 1km Away

[triforce]

Homework Statement

Fans at a stadium produce sound that is heard 1km away, the intensity level is 60 dB. How much acoustic power is generated by the fans?

Homework Equations

B = 10 log (I÷I_0)
P=I*A

The Attempt at a Solution

I= 10^-12*6^10= 10^-6W/m^2
P= 10^-6*4pi*1000^2 =12.56W

However the right answer should be 6.28W

 

[NascentOxygen]

Hi triforce.

Do you need to consider: would sound be absorbed, or reflected, by the stadium floor?

There's a typo in your working, too.

 

[tech99]

Homework Statement

Fans at a stadium produce sound that is heard 1km away, the intensity level is 60 dB. How much acoustic power is generated by the fans?

Homework Equations

B = 10 log (I÷I_0)
P=I*A

The Attempt at a Solution

I= 10^-12*6^10= 10^-6W/m^2
P= 10^-6*4pi*1000^2 =12.56W

However the right answer should be 6.28W

As the sound is radiated into a hemisphere rather than a sphere, the surface area is halved.

 

[triforce]

As the sound is radiated into a hemisphere rather than a sphere, the surface area is halved.

Ah! That makes sense!

Thank you very much!