The loudness of a sound can be approximated by the formula $d=10 \log _{10} \frac{\mathrm{I}}{\mathrm{I}_{\mathrm{O}}}$, where $\mathrm{d}$ is the number of decibels. The higher the value of $d$, the louder the sound. Find the number of decibels when $\mathrm{I}=1000$ and $\mathrm{I}_{\mathrm{O}}=1$.
A) 13 decibels
B) 30 decibels
C) 3 decibels
D) 1000 decibels

Question

Quizplus · Accepted Answer

Plugging in $I = 1000$ and $I_0 = 1$ into the formula $d=10 \log _{10} \frac{I}{I_{O}}$ gives $d = 10 \log_{10} 1000$. Since $\log_{10} 1000 = 3$, the calculation results in $d = 10 \times 3 = 30$ decibels.

The Loudness of a Sound Can Be Approximated by the Formula