Calculating Sound Energy Emission from a Point Source with Constant Power Output

[FsLiu]

Homework Statement

By measurement you determine that sound waves are spreading out equally in all directions from a point source and that the intensity is 2.5×10^−2 W/m^2 at a distance of 4.1m from the source.

How much sound energy does the source emit in one hour if its power output remains constant?

Homework Equations

Not sure, but I just did dimensional analysis since it seems logical: Intensity*Distance^2 gives watts, and the energy in one hour is watts*3600s

The Attempt at a Solution

The answer I got was 1513 J, this is wrong.

 

[fzero]

What shape does the surface at a fixed distance surrounding a point source have? What is the area of the surface for distance d?

 

[FsLiu]

What shape does the surface at a fixed distance surrounding a point source have? What is the area of the surface for distance d?

What I wrote was everything that was given in the question.

In fact, here is a screenshot of the question:

 

[fzero]

What I wrote was everything that was given in the question.

The question gives you all of the information that you need to solve the problem, but you still have to think about what the numbers mean. Intensity is power/area. What is the area that's relevant to the question?

 

[FsLiu]

The question gives you all of the information that you need to solve the problem, but you still have to think about what the numbers mean. Intensity is power/area. What is the area that's relevant to the question?

Buddy, I posted this question here because I KNOW what you just said is true, and I CANT FIGURE IT OUT!

Still looking for an answer.

 

[fzero]

What symmetry does the pattern of sound waves emitted by a point source have?

 

[FsLiu]

What symmetry does the pattern of sound waves emitted by a point source have?

Alright, I'll just restate again that what I thought to be correct was Intensity*Distance^2 gives watts, and the energy in one hour is watts*3600s

Can you just tell me why this is wrong?

 

[fzero]

And I'll restate that intensity is power/area. If you just square 4.1m, what geometrical area does that correspond to? Is that area physically relevant to the problem?

 

[FsLiu]

And I'll restate that intensity is power/area. If you just square 4.1m, what geometrical area does that correspond to? Is that area physically relevant to the problem?

So what you're saying is, I should do pi(4.1^2)?

edit: still doesn't work and I lost another 5% on the assignment.

edit2: still not getting it, but I have a feeling a sphere has something to do with it?

 

[fzero]

So what you're saying is, I should do pi(4.1^2)?

edit: still doesn't work and I lost another 5% on the assignment.

You haven't answered my question, so I suspect you're just trying to guess what formula might be the right one instead of actually thinking about the geometry.

Where did the $$\pi$$ come from? What geometrical area does pi(4.1^2) correspond to?

 

[FsLiu]

You haven't answered my question, so I suspect you're just trying to guess what formula might be the right one instead of actually thinking about the geometry.

Where did the $$\pi$$ come from? What geometrical area does pi(4.1^2) correspond to?

pi(r^2), the area for a circle.

Please just give me a better hint or walk me through how to do it. I honestly have no time for your playing around with me like this with another 4 classes on my hands.

 

[fzero]

I'm sure that all of the people that post responses to homework questions have better things to do with their time too. I'll let your ingratitude slide for the moment...

So pi(r^2) is the area for a circle. Which circle would this be and what does it have to do with the pattern of sound waves emitted by a point source?

What I've been trying to get at from post #2 in this thread is that you need to think about what part of space around the source the power emitted is being transmitted through. Is it a circle somewhere drawn in space or is it something else? I'm sure there's a diagram in your text that would be helpful. Better yet reread the problem because it tells you.

 

[FsLiu]

I'm sure that all of the people that post responses to homework questions have better things to do with their time too. I'll let your ingratitude slide for the moment...

So pi(r^2) is the area for a circle. Which circle would this be and what does it have to do with the pattern of sound waves emitted by a point source?

What I've been trying to get at from post #2 in this thread is that you need to think about what part of space around the source the power emitted is being transmitted through. Is it a circle somewhere drawn in space or is it something else? I'm sure there's a diagram in your text that would be helpful. Better yet reread the problem because it tells you.

I'm sorry for the ingratitude, but physics is killing me since I'm 2 weeks behind as the professor does nothing but write formulas on the board and I understand none of it so I've been teaching myself. In addition, I have 4 other courses equally as difficult, though I'm not behind in them thankfully. Plus you seem to just be toying with me since you know the answer and your hints aren't very helpful.

The question says equally in all directions, so I'm looking at a sphere. The only thing I can think of now after exhausting the possibilities is using the surface area of that sphere.

I don't want to lose another 5% on this question, so please just tell me if that is correct or not.

 

[fzero]

That's correct. We could have come up with that a lot quicker if you'd have just tried answering the first question I asked you.

 

[FsLiu]

That's correct. We could have come up with that a lot quicker if you'd have just tried answering the first question I asked you.

Yeah my brain doesn't work it seems

Thanks.