# How to determine the positions of two points in a radial line by an intensity level dB?

The following is the question from my school.

A source emits sound uniformly in all directions. A radial line is drawn from this source. On this line, determine the positions of two points, 1.00m apart, such that the intensity level at one point is 2.00dB greater than the intensity level at the other.

I have no idea what to do because I haven't met a question about determining the positions by dB.

How can I deal with this question?

Thank you for your attention.

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dB is basically a ratio measurement in logarithmic form.

the sound intensity level $L_1$ is found by applying the following formula to two intensities such as $I_1$ and $I_0$.

$$L_\mathrm{I}=10\, \log_{10}\left(\frac{I_1}{I_0}\right)\ \mathrm{dB} \,$$

i.e, $I_1$ is $L_1~dB$ higher than $I_0$. in your question, $L_1 = 2.00.$

we also know that intensity is proportional to the inverse of distance squared:

$$\frac{I_1}{I_0}=(\frac{r_1}{r_0})^{-2}$$

where $r_1$ is the nearer distance (thus higher intensity). we are also given that $r_1 = r_0+1$

with this you should be able to solve for everything.

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Thank you, the problem has been solved. – Casper LI Oct 6 '13 at 7:57