# Sound Waves

#### ubiquinone

Hi I have a question here from a chapter on sound. I'm not sure on how to solve this, so I was wondering if someone here could please give me a hand. Thank You!!

Question: A point source at $$A$$ emits sound uniformly in all directions. At point $$B$$, the listener measures the sound intensity to be $$50.0dB$$. At point $$C$$, the sound intensity level is $$45.3dB$$. The distance $$\overline{BC}$$ is $$10.0m$$. Calculate the distance $$\overline{AB}$$.

Diagram:
Code:
A----------B
\         |
\       |
\     |
\   |
\ |
C

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#### Hootenanny

Staff Emeritus
Gold Member
Have you any thoughts yourself?

#### ubiquinone

This question is from an old physics exercise book which does not have any examples. I have tried solving it by reading up the concepts on waves and sound from a conceptual physics book. I'm hoping if someone here can show me how to solve this problem, so I can see and understand how a physicist or a good problem solver applies physics concepts and theory into problem solving. Again, any help with this would be greatly appreciated. Thanks!

#### ubiquinone

Hi Hootenanny, thank you for the reference! I think I got it now.

Let $$x$$ be the distance of $$\overline{AB}$$
Calculate the intensities:
$$\displaystyle 50.0dB=10\log\left (\frac{I_1}{10^{-12}}\right )$$
$$\displaystyle\Leftrightarrow 10^5=\frac{I_1}{10^-12}$$
$$\displaystyle\Leftrightarrow 10^{-7}=I_1$$
$$\displaystyle 45.3dB=10\log\left (\frac{I_2}{10^{-12}}\right )$$
$$\displaystyle\Leftrightarrow 10^{4.53}=\frac{I_2}{10^-12}$$
$$\displaystyle\Leftrightarrow 10^{-7.47}=I_2$$
Since $$\displaystyle\frac{I_1}{I_2}=\frac{r_2^2}{r_1^2}\Rightarrow \frac{10^{-7}}{10^{-7.47}}=\frac{\sqrt{x^2+10^2}^2}{x^2}$$
$$\displaystyle\Leftrightarrow 10^{0.47}x^2=x^2+100$$
$$\displaysytle\Leftrightarrow x^2(-1+10^{0.47})=100$$
$$\displaystyle\Rightarrow x=\sqrt{\frac{100}{10^{0.47}-1}}\approx 7.16m$$