The internsity of a particular earthquake wave

[klmdad]

The internsity of a particular earthquake wave is measured to be 2.2 * 10^6 W/m^2 at a distance of 100km from the source. Now here is the part that I'm lost. What was the intensity when it passed a point only 4.0km from the source? And what was the total power passing through an area of 5.0m^2 at a distance of 4.0km?

 

[Davorak]

You can make two different assumptions. that the earthquake's power spreads out from a point on the earth. The power density gets lower and lower the farther you go from the source. This is more then likely what the question is asking for.

If you have a class that likes to pull very hard problems out of nowhere if could be that you have assume that source is a certain distance underground. Then the power dissipation would that follow an easy r^2 or r^3 route. Easiest way to do this would be using spherical coordinates. If you have not used spherical coordinates yet I highly doubt this is the question they are asking.

If I were you I would solve it assuming the source of the earthquake was on the surface. All the power in a 100km radius from the source would then also be present at 4 km away from the source but the perimeter of the circle is smaller so the power density will be higher.

 

[klmdad]

I'm still trying to understand your reply to my Question. If this will helps you to help me it has to do with energy transported by waves. As the wave moves outward, the energy it carries is spread over a larger and larger area since the surface area of asphere of radius r is 4pir^2. Thus the intensity of a wave is I = P/A = P/4pir^2 if we consider two points at distances r1 and r2 from the source then I1 = P/4pir1^2 and I2 = P/4pir2^2, so I2/I1 = r1^2/r2^2

 

[Davorak]

In your original question it was unclear weather you would be dealing with a 2 dimensional problem or a three dimensional problem.

Your second post indicates it is a three dimensional problem deal with a sphere rather then a circle.

What is still unclear is if 100 km is through the ground or over the surface of the ground. This makes a difference since you do not say the depth of the source.

Is the source considered on the surface of the Earth or some distance inside the earth?

From you second post it seems like you know how to correlate a power density from one radius to another, if this is so what difficulty are you having with the problem:?

 

[klmdad]

where I am having problems with is what was the total power passing through an area of 5.0 m^2 at a distance of 4.0 km. I don't see how to work the problem.

 

[Davorak]

You came up with the equation "I2/I1 = r1^2/r2^2", and you know r1 and r2 100km and 4 km and you know I1. So you can solve for I2. Now I2 would be in units of [W/m^2]. You know how many watts per square meter there are, so know all you need to do is figuare out how many watts there are in 5 metters squared.