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!