The sound of a band is rated as $50 \mathrm{~dB}$ at a distance of $30.0 \mathrm{~m}$. What is the sound intensity level of the band when one is $10.0 \mathrm{~m}$ from the band?
A) $52.9 \mathrm{~dB}$
B) $55.2 \mathrm{~dB}$
C) $50.1 \mathrm{~dB}$
D) $57.3 \mathrm{~dB}$
E) $59.5 \mathrm{~dB}$

Question

Quizplus · Accepted Answer

The sound intensity level decreases by $20 \log_{10}(\frac{r_1}{r_2})$ when moving from $r_1$ to $r_2$. Here, $r_1 = 30 \mathrm{~m}$ and $r_2 = 10 \mathrm{~m}$, so the change is $20 \log_{10}(3) \approx 9.54 \mathrm{~dB}$. Adding this to the initial $50 \mathrm{~dB}$ gives approximately $59.5 \mathrm{~dB}$.

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The Sound of a Band Is Rated As $50 \mathrm{~dB}$ At a Distance Of