Question

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as

Answer 1

Answer:

50 Db

Step-by-step explanation:

Given:

$L=10 \log \dfrac{I}{I_0}$

$I_0=10^{-12}$

where:

• L is the loudness measured in decibels (Db)
• I is the sound intensity measured in w/m²

To find the approximate loudness of a dinner conversation with a sound intensity of $I=10^{-7}$, substitute the values of I and I₀ into the given equation and solve for L:

$\implies L=10 \log \dfrac{10^{-7}}{10^{-12}}$

$\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies L=10 \log 10^{-7-(-12)$

$\implies L=10 \log 10^5$

$\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax$

$\implies L=5 \cdot 10 \log 10$

$\implies L=50 \log 10$

As the given log does not have a specified base, assume the base is 10.

$\implies L=50 \log_{10} 10$

$\textsf{Apply log law}: \quad \log_aa=1$

$\implies L=50 (1)$

$\implies L=50\:\:\sf Db$

Learn more about log laws here:

brainly.com/question/27963321

brainly.com/question/28016999

Answer 2

$\\ \rm\dashrightarrow B=10log\dfrac{I}{I_o}$

$\\ \rm\dashrightarrow B=10\log\dfrac{10^{-7}}{10^{-12}}$

$\\ \rm\dashrightarrow B=10log10^5$

$\\ \rm\dashrightarrow B=10\times 5log10$

$\\ \rm\dashrightarrow B=10(5)$

$\\ \rm\dashrightarrow B=50dB$