Figuring out changes in Intensity (Inverse Square Law)

In summary, the inverse square law for intensity vs distance states that the intensity at a distance of 3R would be 9 times less than at a distance of R. In terms of decibels, this translates to a difference of 9.54 dB using the formula 10(log(9)). However, this formula does not account for the "inverse" and "square" properties, so it is not accurate.
  • #1
RichardGib
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Homework Statement



If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels?

Homework Equations



I know that the equation for this is 10 (log R2/R1)

The Attempt at a Solution



I thought that the answer could be a 9.54 dB difference. I did: 10(log(9) to figure this out but the answer doesn't seem correct. Any help with answering this question would be greatly appreciated. Thank you
 
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  • #2
Intensity follows an inverse square law with distance. So you'd expect the intensity at 3R to be 9 times less than the intensity at R, right? So the inverse square law for intensity vs distance looks like:
$$\frac{I_2}{I_1} = \frac{R_1^2}{R_2^2}$$
Decibels are a comparison of intensities, so if you want to use the distances in the decibel formula rather than the intensities you need to remember to keep the inverse square law in mind and employ the squares of the distances and the "inverse" property as well. That said, take a look at the ratio above and then your Relevant equation. Does your equation preserve the "inverse" and "square" properties?
 

What is the Inverse Square Law and how does it apply to changes in intensity?

The Inverse Square Law is a principle in physics that states the intensity of a physical quantity (such as light or sound) is inversely proportional to the square of the distance from the source. This means that as the distance from the source increases, the intensity decreases.

How do I calculate changes in intensity using the Inverse Square Law?

To calculate changes in intensity using the Inverse Square Law, you will need to know the initial intensity and the distance from the source. Then, you can use the formula I1/I2 = (d2/d1)^2, where I1 is the initial intensity, I2 is the final intensity, d1 is the initial distance, and d2 is the final distance.

What are some real-life examples of the Inverse Square Law?

Some common examples of the Inverse Square Law include the brightness of a light bulb, the loudness of a speaker, and the strength of gravitational or electric fields. In all of these cases, the intensity decreases as the distance from the source increases.

How does the Inverse Square Law relate to radiation and radioactive decay?

The Inverse Square Law is commonly used in the field of radiation and radioactive decay. As radioactive particles decay, the intensity of the radiation decreases according to the Inverse Square Law. This is why it is important to maintain a safe distance from radioactive materials to minimize exposure.

Are there any exceptions to the Inverse Square Law?

The Inverse Square Law is a general principle and there may be some exceptions depending on the specific situation. For example, in cases where there are multiple sources of radiation, the Inverse Square Law may not apply. It is important to carefully consider the conditions and factors involved when applying the Inverse Square Law.

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