The loudness of a sound can be quantified in units called decibels, where the number of decibels 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) 13 decibels
B) 3 decibels
C) 30 decibels
D) 1000 decibels

Question

Quizplus · Accepted Answer

The formula for calculating decibels is $d = 10 \log \frac{I}{I_0}$. Substituting $I = 1000I_0$ into the formula gives $d = 10 \log 1000 = 10 \log 10^3 = 10 \times 3 = 30$ decibels.

The Loudness of a Sound Can Be Quantified in Units d=10log⁡II0\mathrm { d } = 10 \log \frac { \mathrm { I } } { \mathrm { I } _ { 0 } }d=10logI0​I​

The Loudness of a Sound Can Be Quantified in Units $\mathrm { d } = 10 \log \frac { \mathrm { I } } { \mathrm { I } _ { 0 } }$