Calculating Total Power Output of a Speaker at a Given Distance

[FunkyFrap]

Homework Statement

A speaker emits sound waves in all directions, and at a distance of 28 m from it the intensity level is 73 db. What is the total power put out by the speaker, in watts? ( reference intensity $I_{0}$ is 1.0 × 10-12 W/m2.)

Homework Equations

$P= I*A$
$I = I_{0}*10^{B/10}$
$SA = 4*pi*r^{2}$

The Attempt at a Solution

Since we're looking for the total power of the speaker, I first used equation 2 to find the intensity, $I$. For $B = 73 db$ and $I_{0} = 10^{-12} W*m^{-2}$ I obtained $I = 2*10^{-5} W*m^{-2}$ .

Then the area is $A = 4*pi*(28)^{2} m^{2} = 9852.03 m^{2}$

Therefore, the total Power is
$P = I*A = 0.197 W$

So that's my attempt but I'm still not entirely confident in that answer. I'm not too sure if the Area equation I'm using is correct. It says in all directions hence why I used surface area but now I'm thinking it's $A = pi*r^2$.

Is that right? Or was the surface area equation the correct one to use?

 

[TSny]

You were correct in your original calculation. Is there a reason why you were thinking that maybe you should use the area of a circle rather than the surface area of a sphere?

 

[FunkyFrap]

You were correct in your original calculation. Is there a reason why you were thinking that maybe you should use the area of a circle rather than the surface area of a sphere?

I imagined the speaker on the ground, and then imagine the 'sphere' of sound in all directions. I didn't see it as a full sphere, so I thought the first equation wasn't right. Then I guessed it might just be a circle.

 

[TSny]

OK. Does it make sense now?

 

[FunkyFrap]

OK. Does it make sense now?

Yes it does. Thank you very much!