Solve the problem.
-The loudness of a sound can be quantified in units called decibels, where the number of decibels $\mathrm { d }$ is given by the formula $\mathrm { d } = 10 \log \frac { \mathrm { I } } { \mathrm { I } _ { 0 } }$.
What is the decibel rating of a sound having an intensity $\mathrm { I } = 1000 \mathrm { I } _ { 0 }$ ?
A) 1000 decibels
B) 3 decibels
C) 30 decibels
D) 13 decibels

Question

Quizplus · Accepted Answer

The decibel rating is calculated using the formula $d = 10 \log \frac{I}{I_0}$. Substituting $I = 1000I_0$ into the formula gives $d = 10 \log 1000$. Since $\log 1000 = 3$ (because $10^3 = 1000$), the calculation yields $d = 10 \times 3 = 30$ decibels.

Solve the Problem d\mathrm { d }d Is Given by the Formula

Solve the Problem $\mathrm { d }$ Is Given by the Formula