Solve the problem.
-The loudness of a sound can be quantified in units called decibels, where the number of decibels d is given by the formula $d = 10 \log \frac { I } { I _ { 0 } }$.
What is the decibel rating of a sound having an intensity $I = 100 \mathrm { I } _ { 0 }$ ?
A) 2 decibels
B) 20 decibels
C) 100 decibels
D) 12 decibels

Question

Quizplus · Accepted Answer

The decibel rating is calculated using the formula $d = 10 \log \frac { I } { I _ { 0 } }$. Substituting $I = 100I_0$ into the formula gives $d = 10 \log \frac { 100I_0 } { I _ { 0 } } = 10 \log 100$. Since $\log 100 = 2$, the calculation yields $d = 10 \times 2 = 20$ decibels.

Solve the Problem d=10log⁡II0d = 10 \log \frac { I } { I _ { 0 } }d=10logI0​I​

Solve the Problem $d = 10 \log \frac { I } { I _ { 0 } }$