Power output and sound intensity

[dylanwalt]

Homework Statement

At a distance of 2.5m from your stereo system with two speakers, the intensity level is 78 dB. Assume that all the energy from the amplifier goes into producing sound. What power output does your stereo have?

Relevant Equations

B=10log I/Ith

In the picture below

 

[haruspex]

Why did you change $4\pi r^2$ to $\pi r^2$?

 

[Mister T]

We're assuming the two speakers are point sources that share the same location?

 

[haruspex]

We're assuming the two speakers are point sources that share the same location?

Good point. More likely, the speakers are 2.5m either side of the listener.

 

[dylanwalt]

Why did you change $4\pi r^2$ to $\pi r^2$?

I was not sure if the question was in 2d hence pi*r*r or 3d 4*pi*r*r.

 

[dylanwalt]

Good point. More likely, the speakers are 2.5m either side of the listener.

I’m not 100% sure it is a vague question. I assumed they were in the same speaker housing maybe one was bass and one treble etcetera.

 

[haruspex]

I was not sure if the question was in 2d hence pi*r*r or 3d 4*pi*r*r.

We do not live in Flatland.

I’m not 100% sure it is a vague question. I assumed they were in the same speaker housing maybe one was bass and one treble etcetera.

It mentions specifically "two speakers", and stereo systems are not just a matter of separate woofers and tweeters; typically, a stereo system has two speaker housings, each containing a tweeter and a woofer.
The separation of stereo speakers would commonly be around 2.5m, suggesting an equilateral triangle arrangement.
However, it's not clear to me how that would affect the answer, so just take it as a point source.

 

[berkeman]

The separation of stereo speakers would commonly be around 2.5m, suggesting an equilateral triangle arrangement.
However, it's not clear to me how that would affect the answer, so just take it as a point source.

Yeah, this is a very confusing problem statement.

We do not live in Flatland.

LOL.

 

[berkeman]

I was not sure if the question was in 2d hence pi*r*r or 3d 4*pi*r*r.

Please check your Private Messages (PMs) in a minute or two. I will send you some tips for learning and using LaTeX to post math equations at PF.

 

[Mister T]

Speaker cabinets contain at least one driver, like say a woofer and a tweeter. By their very design they are not point sources. In my opinion that's the most unrealistic feature of the problem statement.