the loudness, l, measured in decibels (db), of a sound intensity, i, measured in watts per square meter, is…

the loudness, l, measured in decibels (db), of a sound intensity, i, measured in watts per square meter, is defined as $l = 10\\log\\frac{i}{i_0}$, where $i_0 = 10^{-12}$ and is the least intense sound a human ear can hear. brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. the sound intensity level that brandon can hear is $10^{-10}$. ahmad, brandons neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is $10^{-4}$. how does brandons sound intensity level compare to ahmads mower?\no brandons sound intensity is $\\frac{1}{4}$ the level of ahmads mower.\no brandons sound intensity is $\\frac{1}{6}$ the level of ahmads mower.\no brandons sound intensity is 20 times the level of ahmads mower.\no brandons sound intensity is 80 times the level of ahmads mower.

the loudness, l, measured in decibels (db), of a sound intensity, i, measured in watts per square meter, is defined as $l = 10\\log\\frac{i}{i_0}$, where $i_0 = 10^{-12}$ and is the least intense sound a human ear can hear. brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. the sound intensity level that brandon can hear is $10^{-10}$. ahmad, brandons neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is $10^{-4}$. how does brandons sound intensity level compare to ahmads mower?\no brandons sound intensity is $\\frac{1}{4}$ the level of ahmads mower.\no brandons sound intensity is $\\frac{1}{6}$ the level of ahmads mower.\no brandons sound intensity is 20 times the level of ahmads mower.\no brandons sound intensity is 80 times the level of ahmads mower.

Answer

Answer:

Brandon's sound intensity is $\frac{1}{10^{6}}$ the level of Ahmad's mower.

Explanation:

Step1: Identify Brandon's sound intensity

Brandon's sound intensity $I_{B}=10^{- 10}$.

Step2: Identify Ahmad's sound intensity

Ahmad's sound intensity $I_{A}=10^{-4}$.

Step3: Calculate the ratio

The ratio of Brandon's sound intensity to Ahmad's is $\frac{I_{B}}{I_{A}}=\frac{10^{-10}}{10^{-4}}$. Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\frac{10^{-10}}{10^{-4}}=10^{-10-(-4)}=10^{-6}=\frac{1}{10^{6}}$. So Brandon's sound intensity is $\frac{1}{10^{6}}$ the level of Ahmad's mower.